MUTHAYAMMAL ENGINEERING COLLEGE

(An Autonomous Institution)

(Approved by AICTE, New Delhi, Accredited by NAAC & Affiliated to Anna University)
Rasipuram - 637 408, Namakkal Dist., Tamil Nadu

LECTURE HANDOUTS L 01

Physics I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : I Acoustics & Ultrasonics Date of Lecture:

Topic of Lecture: Introduction of acoustics,Classification of sound,Weber Fechner law

Introduction:
 Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids,
and solids including topics such as vibration, sound, ultrasound and infrasound.

 A scientist who works in the field of acoustics is an acoustician while someone working in the
field of acoustics technology may be called an acoustical engineer.

 The application of acoustics is present in almost all aspects of modern society with the most
obvious being the audio and noise control industries.

Prerequisite knowledge for Complete understanding and learning of Topic:

 Basic knowledge on acoustics
 Audible range of frequency
Detailed content of the Lecture:
Introduction of acoustics
 Acoustics is the science of sound which deals with origin, propagation and properties of sound
waves.
 Sound is produced by a vibrating body and it cannot travel in vacuum, this requires the medium
for its propagation. Sound waves are longitudinal waves in nature.
 Acoustics is defined as the “Science of sound”, Understanding sound as a mechanical disturbance
in an elastic and inertial medium.
 These disturbances or oscillations of air pressure are converted into mechanical waves which
excite the auditory mechanism, resulting in a perception. Sound intensity is measured in Decibels
(dB).
Classification Of Audible Sound
i). Musical sound:
 They are regular in shape
 They have periodicities
 Change in amplitude is uniform
 ii). Noise sound
 They are irregular in shape
 They are not periodic
 Change in amplitude is not uniform
CHARACTERISTICS OF MUSICAL SOUND
The characteristics of the musical sound are:
 Frequency or pitch
 Frequency is defined as the number of vibrations produced per second. Greater the frequency of
a musical note, the higher is the pitch and vice versa. Frequency is a measurable physical
quantity and it can be measured accurately.
 Intensity or loudness
 Intensity of sound wave at a point is defined as the energy flowing per second per unit area hold
normally at a point to the direction of propagation of sound wave.
 Timbre or quality
 The quality of a sound wave is the ability to distinguish the musical notes emitted by two or
more than two musical instruments, even though they have the same pitch and loudness.
WEBER-FECHNER LAW
 This law relates the intensity of sound waves with loudness.
 This law states that the sound is proportional to the logarithm of the sound intensity.
 If L is the degree of loudness due to intensity I,
 L = K log I
 Where, the K is a constant. Greater the intensity of sound, the loudness is greater.
Video Content / Details of website for further learning (if any):
 https://www.khanacademy.org/science/health-and-medicine/nervous-system-and-sensory-
infor/sensory-perception-topic/v/webers-law-and-thresholds
 https://www.youtube.com/watch?v=1JtuksSrdhc
Important Books/Journals for further learning including the page nos.:
 G. Sudarmozhi, Engineering Physics, Sri Kandhan publications, 2005, Page no. 2.1-2.5

Course Faculty

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 MUTHAYAMMAL ENGINEERING COLLEGE
(An Autonomous Institution)
(Approved by AICTE, New Delhi, Accredited by NAAC & Affiliated to Anna University)
Rasipuram - 637 408, Namakkal Dist., Tamil Nadu

LECTURE HANDOUTS L 02

Physics I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : I Acoustics & Ultrasonics Date of Lecture:

Topic of Lecture: Reverberation , Reverberation time, Factors affecting acoustics of building and its
Remedy
Introduction :
 When a sound is produced in a building, it persists too long after its production. The sound
generated travels towards the wall, floor, ceiling etc and are reflected back. Persistence of
audible sound after the source has stopped to emit sound in the hall is called reverberation.

Prerequisite knowledge for Complete understanding and learning of Topic:

 Basic knowledge on reverberation
 Factors controlling the reverberation time

Detailed content of the Lecture:

Reverberation
 Sound persists for some time after the original sound from the source is stopped.
 Persistence of audible sound after the source has stopped to emit sound in the hall is called
reverberation.
 A listener inside the hall receives the sound till the intensity of the sound wave becomes inaudible.

Reverberation time
 The duration for which the sound persists in a hall is called reverberation time.
 The standard reverberation time is defined as the time taken by sound to fall to one millionth of its
intensity just before the source is cutoff.
Em
E 
106
Where, E is the energy of the sound at any time t and E m is the maximum sound energy produced
before the source is cut off.
  The time of reverberation depends on various factors like size of the hall, loudness of the sound
kind of music or the sound for which the hall is used etc.
 According to Sabine, the reverberation time is given by
0.165V
T  sec onds
A
 Where, V is the volume of the hall and A is the total observation.
 Total absorption of any hall is given as A   a s
Factors affecting the acoustics of a building and their remedies
 Reverberation
i) Providing windows and ventilators
ii) Using curtains with full folding to increase the area
 Loudness
i) Loudness can be increased by providing necessary reflecting surfaces and loud speakers
wherever the loudness is insufficient.
ii) Sound absorbing materials should be provided where the loudness is higher in the hall
 Echoes
i) By providing sufficient number of doors and windows, this effect can be minimized
ii) Providing high ceiling in a hall can reduce the effect echo
 Echelon effect
i) This effect should be avoided by providing sound absorbing materials on its surface.
 Resonance
i) The resonant vibrations should be avoided by maintaining the optimum level of reverberation
time
ii) This can be reduced by providing proper ventilations
 Noises
i) The outside noises can be controlled by providing proper doors and windows, using double door
and double walls
ii) The noises produced inside the hall can be controlled by providing anti vibration mounts
Video Content / Details of website for further learning (if any):
 https://www.cirrusresearch.co.uk/blog/2018/04/what-is-reverberation-time-and-how-it-is-
calculated/
 https://www.ques10.com/p/14361/what-is-reverberation-define-reverberation-time-ex/
Important Books/Journals for further learning including the page nos.:
 G. Sudarmozhi, Engineering Physics, Sri Kandhan publications, 2005, Page no. 2.6

Course Faculty

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 MUTHAYAMMAL ENGINEERING COLLEGE
(An Autonomous Institution)
(Approved by AICTE, New Delhi, Accredited by NAAC & Affiliated to Anna University)
Rasipuram - 637 408, Namakkal Dist., Tamil Nadu

LECTURE HANDOUTS L 03

Physics I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : I Acoustics & Ultrasonics Date of Lecture:

Topic of Lecture: Absorption coefficient, Measurement of Absorption coefficient

Introduction:
 The coefficient of absorption (a) of a material is defined as the ratio of sound energy absorbed
by the surface to that of total sound energy incident on the surface .
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on sound absorbing materials,absorption coefficient
Detailed content of the Lecture:
COEFFICIENT OF ABSORPTION (OR) ABSORPTION COEFFICIENT
 Different surfaces of an auditorium absorb sound to different extents.
 An open window transmits the entire sound energy falling on its surface where no reflection of sound is
absorbed.
 In the case of material surfaces, the sound energy is partly absorbed and partly reflected.
 The coefficient of absorption (a) of a material is defined as the ratio of sound energy absorbed by the surface
to that of total sound energy incident on the surface.
Sound energy absorbed by the surface
a 
Total sound energy incident on the surface
 Since the open window is fully transmitting the sound incident on it, it is considered as an ideal sound
absorber.
 Thus the unit of absorption is the open window unit (OWU) and is named as ‘sabine’ after the scientist who
established the unit.
Absorption coefficient of some materials
The absorption coefficient of some of the materials is given in the table.
Absorption
S. No Materials
Coefficient/m2
1 Open window 1.00
2 Stage curtain 0.2
3 Curtain with folds 0.4 - 0.75
4 Carpet 0.4
5 An audience 0.46
6 Perforated fiber board 0.55
Determination of absorption coefficient
 Absorption coefficient of any material can be determined by placing the material inside the room.
Initially the room is kept empty and its reverberation time is assumed to be T 1.
0.165V
Then T1  --------- (1)
A
 Where, V is the volume of the hall and A is the total absorption inside the hall due to walls, flooring
and ceiling.
 Then the sound absorbing material of area S and absorption coefficient α’ is placed inside the room
and again the reverberation time (T2) is measured using the equation (2)
0.165V
T2 
A   'S --------- (2)

Subtracting equation (1) from Equation (2), we get

0.165V 0.165V
T2  T1  
A   'S A
0.165V

 'S
0.165V
or '  ---- (3)
S (T2  T 1)

Knowing the values on R.H.S of equation (3), the absorption coefficient  ' of the material under test
can be calculated.

Video Content / Details of website for further learning (if any):

 https://www.pveducation.org/pvcdrom/pn-junctions/absorption-coefficient
 http://www.acoustic-glossary.co.uk/sound-absorption.htm
Important Books/Journals for further learning including the page nos.:
 G. Sudarmozhi, Engineering Physics, Sri Kandhan publications, 2005, Page no. 2.9-2.12

Course Faculty

Verified by HOD
 MUTHAYAMMAL ENGINEERING COLLEGE
(An Autonomous Institution)
(Approved by AICTE, New Delhi, Accredited by NAAC & Affiliated to Anna University)
Rasipuram - 637 408, Namakkal Dist., Tamil Nadu

LECTURE HANDOUTS L 04

Physics I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : I Acoustics & Ultrasonics Date of Lecture:

Topic of Lecture: Introduction to Ultrasonics and properties

Introduction :
 Ultrasonic wave has different properties for example, ultrasonic waves produce stationary wave
pattern in the liquid while passing through it.
 These waves can be detected by various methods and will be discussed
Prerequisite knowledge for Complete understanding and learning of Topic:
 Knowledge on properties of ultrasonic waves
 Methods on detection of ultrasonic waves
Detailed content of the Lecture:
Introduction to Ultrasonics
 Human ear is capable of receiving the sound waves with frequency range of 20Hz to 20,000Hz.
 The frequency ranges below 20Hz and above 20,000Hz are inaudible to human being.
 Based on the frequency, sound waves are generally classified into three types:
i) Infrasonic waves
ii) Audible range of frequency and
iii) Ultrasonic waves
 The sound waves having frequency below 20Hz are called infrasonic sound.
 The sound waves having frequency 20Hz to 20000 Hz are said to be audible sound.
 The sound waves having frequency more 20000 Hz are called ultrasonic waves.
Properties of ultrasonic waves
 They are highly energetic
 They are longitudinal in nature
 Ultrasonic waves undergo reflection, refraction and diffraction like sound waves
 When ultrasonic waves passed through the liquids, stationary wave patterns are produced and it behaves
as acoustical grating element
 When an object is exposed to ultrasonic for longer time it produces heating effect
  By increasing the frequency of ultrasonic waves, energy can be increased
 They produce cavitation effect in liquids
 They can travel over long distances without any loss of energy
 Ultrasonic waves are high frequency and high energetic sound waves.
 Ultrasonic waves produce negligible diffraction effects because of their small wavelength.
 Ultrasonic wave travels longer distance without any energy loss.
 The speed of propagation of ultrasonic waves increases with the frequency of the waves.
 At room temperature, ultrasonic welding is possible.
 Ultrasonic waves produce cavitation effects in liquids.
 Ultrasonic waves produce acoustic diffraction in liquids.
 Ultrasonic waves cannot travel through the vacuum.
 Ultrasonic waves travel with speed of sound in a given medium.
 Ultrasonic waves require one material medium for its propagation.
 Ultrasonic waves can produce vibrations in low viscosity liquids.
 Ultrasonic waves produces heat effect passes through the medium.
 Ultrasonic waves obey reflection, refraction, and absorption properties similar to sound waves.
 When the ultrasonic wave is absorbed by a medium, it generates heat. They are able to drill and
cut thin metals.

Video Content / Details of website for further learning (if any):

 http://www.vidyarthiplus.in/2011/11/engineering-physics-1-ultrasonics.html
 https://www.youtube.com/watch?v=hivv2hgqDvk
Important Books/Journals for further learning including the page nos.:
 G. Sudarmozhi, Engineering Physics, Sri Kandhan publications, 2005, Page no. 2.8-2.9

Course Faculty

Verified by HOD
 MUTHAYAMMAL ENGINEERING COLLEGE
(An Autonomous Institution)
(Approved by AICTE, New Delhi, Accredited by NAAC & Affiliated to Anna University)
Rasipuram - 637 408, Namakkal Dist., Tamil Nadu

LECTURE HANDOUTS L 05

Physics I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : I Acoustics & Ultrasonics Date of Lecture:

Topic of Lecture: Detection of ultrasonic waves, Magnetostriction effect - Magnetostriction generator

Introduction :
When an alternating magnetic field is applied to a bar of ferromagnetic materials, it
undergoes a change in dimension there by producing ultrasonic waves at resonance is called
Magnetostriction effect (or) Magnetostriction principle.
Prerequisite knowledge for Complete understanding and learning of Topic:
 Magnetostriction effect
 Construction working of Magnetostriction generator
Detailed content of the Lecture:
Detection of ultrasonic waves
 The presence of ultrasonic waves can be detected by the following methods.
 Piezo electric method,Kundt’s tube method,Sensitive flame method,Thermal method
Magnetostriction effect
 When a bar of ferromagnetic material, like nickel, cobalt etc. is placed in an alternating magnetic field
parallel to its length, it undergoes slight change in dimension.
 This change in length is independent of the field and may be decreased or increased depending on the
materials.
 With high frequency alternating magnetic field, the bar contracts and expands alternatively and begins to
vibrate to and fro and producing ultrasonic waves at its ends.
Magnetostriction generator
Working
 The battery is switched on and hence current is produced by the transistor. This current is passing
through the coil L which in turn causes magnetic effect over the rod.
 Because of the magnetic effect, the rod starts vibrating due to magnetostriction effect. When the rod
is vibrating, an e.m.f is induced in the coil L1..
 The induced e.m.f. is fed into the base of the transistor which acts as a feed back for the circuit. In
this way, the current in the transistor is built up and the vibration of the rod is maintained.
 The frequency of the oscillatory circuit is adjusted by the variable capacitor C.
 When the frequency of the oscillatory circuit becomes equal to the natural frequency of the
rod, resonance effect occurs. At the resonance condition, the rod vibrates with larger amplitude,
producing high frequency ultrasonic waves at both the ends of the rod.
 The frequency of the oscillatory circuit is given as
1
2 LC
 The natural frequency of the ferromagnetic rod is given as
1 E
2l 
Where l is the length of the rod,E is the Young’s modulus of the rod and ρ is the density of material
of the rod
The ultrasonic waves are produced when,
The frequency of the oscillatory circuit = The natural frequency of the rod
1 1 E
=
2 LC 2l 
Advantages
 The design of the oscillatory circuit is very simple and its production cost is low
 At low frequencies, large power output is possible without causing any damage to the oscillatory
circuit
Disadvantages
 It can produce frequencies up to 3MHz only
 The frequency of oscillations depends on the temperature
 As the frequency is inversely proportional to the length of the rod, the length of the rod should be
decreased to increase the frequency which is practically impossible.

Video Content / Details of website for further learning (if any):

 https://www.brainkart.com/article/Magnetostriction-Method--Principle,-Construction,-
working,-Advantages-and-Limitations_6871/
 https://www.youtube.com/watch?v=Kb_uB3GXGwg

Important Books/Journals for further learning including the page nos.:

 G. Sudarmozhi, Engineering Physics, Sri Kandhan publications, 2005, Page no. 2.20-2.22

Course Faculty

Verified by HOD
 MUTHAYAMMAL ENGINEERING COLLEGE
(An Autonomous Institution)
(Approved by AICTE, New Delhi, Accredited by NAAC & Affiliated to Anna University)
Rasipuram - 637 408, Namakkal Dist., Tamil Nadu

LECTURE HANDOUTS L 06

Physics I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : I Acoustics & Ultrasonics Date of Lecture:

Topic of Lecture: Piezoelectric effect - piezoelectric generator,

Introduction :
 The piezoelectric effect was discovered in 1880 by two French physicists, brothers Pierre and
PaulJacques Curie, in crystals of quartz, tourmaline, and Rochelle salt (potassium sodium
tartrate).
 This phenomenon is observable in many naturally available crystalline materials, including
quartz, Rochelle salt and even human bone.
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on piezoelectric effect
 Piezoelectric generator
Detailed content of the Lecture:
Principle
 When a crystal like (calcite or quartz) under goes mechanical deformation along the mechanical
axis then electric potential difference is produced along the electrical axis perpendicular to
mechanical axis. This phenomenon is known as piezoelectric effect.

 The converse of the effect is also possible.

 When an alternative potential is applied along the electrical axis, the crystal will set into electric
vibrations along the mechanical axis.
 If the frequency of the crystal is equal to the natural frequency of the crystal, it vibrates with larger
amplitude producing ultrasonics.
  The quartz crystal between the metal plates is connected to collector and base of transistor.
 Collector is also connected to LC circuit and high tension source shunted a by pass capacitor C b.
 Cb is used to stop high frequency currents from passing through battery.
 The capacity of variable capacitor is adjusted so that the frequency of the oscillating circuits is
 equal to the natural frequency of the crystal. R g provided necessary biasing for base and emitter circuit.
 When the circuit is starts functioning slowly an alternative potential difference is built across the quartz
crystal which sets the crystal into vibrations.
 By varying the capacitor of capacitor C, at a particular stage the frequency of the alternating potential
across the crystal coincides with the natural frequency of the quartz crystal it to produce ultrasonic
waves.
 This stage is indicated by milli ammeter by showing maximum current.
 The natural frequency of quartz crystal of thickness t is given by

 Where y is young’s modulus and ρ is the density of crystal

Video Content / Details of website for further learning (if any):

 https://www.youtube.com/watch?v=4nbBAG-848c
 https://www.youtube.com/watch?v=fHp95e-CwWQ
Important Books/Journals for further learning including the page nos.:
 G. Sudarmozhi, Engineering Physics, Sri Kandhan publications, 2005, Page no. 2.14-2.16

Course Faculty

Verified by HOD
 MUTHAYAMMAL ENGINEERING COLLEGE
(An Autonomous Institution)
(Approved by AICTE, New Delhi, Accredited by NAAC & Affiliated to Anna University)
Rasipuram - 637 408, Namakkal Dist., Tamil Nadu

LECTURE HANDOUTS L 07

Physics I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : I Acoustics & Ultrasonics Date of Lecture:

Topic of Lecture: Cavitation ,SONAR

Introduction:
 In general, cavitation is the phenomenon where small and largely empty cavities are
generated in a fluid, which expand to large size and then rapidly collapse. When the
cavitation bubbles collapse, they focus liquid energy to very small volumes.
 Sonar is based on the echo-sounding technique of ultrasound. When an ultrasonic wave is
transmitted through water, it is reflected by the objects in the water and will produce an
echo signal
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on SONAR
 Basic knowledge on Cavitation
Detailed content of the Lecture:
Cavitation
 In a liquid, the bubbles in the order of 10–9 to 10–8 m sizes are always present.
 The decrease in pressure above the liquid causes evaporation in the bubbles and leads to their
growth.
 The growth of bubble leads to their collapse with in few milliseconds and release very large
amount of pressure and temperature.
 During the collapse of the bubble, temperature of the gas within the bubble is increases abruptly at
about 10, 000°C.
 Ultrasonic waves while passing through the liquid medium induce compression and rarefaction
and create millions of microscopic low pressure bubble.
 A negative local pressure at the rarefaction causes local boiling of the liquid accompanied by the
bubble growth and it gets collapse. This phenomenon is known as cavitation.
 Cavitation is the process of creation and collapse of bubbles due to negative local pressure created
inside the bubble.

SONAR
 Sonar is based on the echo-sounding technique of ultrasound.
 When an ultrasonic wave is transmitted through water, it is reflected by the objects in the water
and will produce an echo signal.
 By noting the time interval between the generation of the ultrasonic pulse and the reception of the
echo signal (t), the depth of the object can be easily calculated.
  Since the ultrasonic velocity “v’ in sea water is known, the depth of sea is calculated as follows
Depth of sea (distance between surface and bottom of the sea) = vt/2

 The same procedure is also used to find the distance of submarine or iceberg from the surface of
the sea and the distance between two ships in the sea.

Video Content / Details of website for further learning (if any):

 https://www.youtube.com/watch?v=4nbBAG-848c
 https://www.youtube.com/watch?v=fHp95e-CwWQ
Important Books/Journals for further learning including the page nos.:
 G. Sudarmozhi, Engineering Physics, Sri Kandhan publications, 2005, Page no. 2.16-2.20

Course Faculty

Verified by HOD
 MUTHAYAMMAL ENGINEERING COLLEGE
(An Autonomous Institution)
(Approved by AICTE, New Delhi, Accredited by NAAC & Affiliated to Anna University)
Rasipuram - 637 408, Namakkal Dist., Tamil Nadu

LECTURE HANDOUTS L 08

Physics I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : I Acoustics & Ultrasonics Date of Lecture:

Topic of Lecture: Non Destructive Testing pulse echo system and through transmission

Introduction:
 Non-destructive testing defines and locates flaws within a material without destroying or
defacing the product.
 Ultrasonic non-destructive testing is one of the major tests to find out the defects, cracks and
discontinuities in a medium.
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on NDT and its applications
Detailed content of the Lecture:
Non-Destructive Testing
 Ultrasonic energy striking at an interface of two different materials is partially reflected and
partially transmitted.
 The transmitted energy in the medium is utilized for the inspection purpose.
 Depends on the information required, a number of techniques are used for the ultrasonic
inspection. Some of the important testing techniques are,
1) Pulse-echo method,2)Through transmission method and 3)Resonance method.
Pulse-echo method
 In this method, high frequency ultrasonic waves are generated with the help of piezoelectric
crystal and transmitted into the material under testing.
 The principle of reflection of ultrasonic waves at the interface of two different media is used in
this method.
 The reflected sound waves are received by the transducers and converted into electrical energy.
 If the material does not have any flaws inside, the pulses produced in the CRO is as shown in the
Figure.
 Two pulses, one is due to the reflection at the front surface and the other is due to the reflection at
the back surface of the material are produced.

 If the material has a flaw in the path of ultrasonic waves, one additional reflection is produced as
shown in the Fig. It shows that there is an acoustical impedance mismatch in the path of ultrasonic
waves.
 Using the amplitude and time of travel through the material, the length of the specimen or the
distance at which the flaw is located can be determined.
 In this method a single transducer can be used to transmit and receive the signals.
Through transmission method
 In this method two transducers are used in which one acts as transmitter (T) and the other acts as a
receiver (R).
 The transmitter and receiver are connected in the opposite sides of the specimen which is under
testing.
 The ultrasonic beam from the transmitter travel through the material to the opposite face and is
received by a receiver.
 The received ultrasonic waves are converted into electrical pulses and then fed into the CRO.
 Any defect in the path of the ultrasonic beam can produce reduction of sound energy reaching the
receiver.

 The material with no defect produces the pulses of same height in the CRO as shown in Figure.
The existence of flaw in the material can be identified by reduction of sound energy (smaller
pulse) as shown in Figure.
 Thus the defects presents inside the material can be studied using this method.
 The main disadvantage of this system is it does not give the information about exact size and
location of the defect. It is useful for the inspection of large castings and where the gross defects
are present.
Video Content / Details of website for further learning (if any):
 http://dx.doi.org/10.6028/NBS.TN.1199
 https://ndt-testing.org/our-services/ultrasonic-testing-pulse-echo-method/
 https://www.google.com/search?q=pulse-
echo+method+pdf&sa=X&ved=2ahUKEwjSm_SUzMfoAhX0wjgGHRaUATQQ1QIoAXo
ECAwQAg
Important Books/Journals for further learning including the page nos.:
 G. Sudarmozhi, Engineering Physics, Sri Kandhan publications, 2005, Page no. 2.29 and
2.23

Course Faculty

Verified by HOD
 MUTHAYAMMAL ENGINEERING COLLEGE
(An Autonomous Institution)
(Approved by AICTE, New Delhi, Accredited by NAAC & Affiliated to Anna University)
Rasipuram - 637 408, Namakkal Dist., Tamil Nadu

LECTURE HANDOUTS L 09

Physics I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : I Acoustics & Ultrasonics Date of Lecture:

Topic of Lecture: Non Destructive Testing resonance method

Introduction:
 Non-destructive testing defines and locates flaws within a material without destroying or defacing the
product. Ultrasonic non-destructive testing is one of the major tests to find out the defects, cracks and
discontinuities in a medium.
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on NDT and its applications

Detailed content of the Lecture:

• Non-destructive testing defines and locates flaws within a material without destroying or defacing the
product.
Important testing techniques
• Pulse-echo method
• Through transmission method
• Resonance method
Resonance method
• The system consists of a transducer which is connected to the specimen and a CRO with transmitting and
receiving signals.
• The transducer produces an ultrasonic wave (longitudinal wave) which is transmitted through the
specimen. These waves get reflected between the opposite faces of a specimen. The probe is moved on
the surface of the material to study the resonant frequency.
• The frequency of this longitudinal wave is varied continuously till the standing waves are setup in the
material. Standing waves are created by adjusting the frequency of the ultrasonic waves.
• The frequency of the longitudinal wave is varied continuously till the standing waves are setup in the
material. Standing waves are created by adjusting the frequency of the ultrasonic waves.
• Due to the formation of standing waves inside the specimen, the material vibrates at its resonance
frequency with maximum amplitude.
 •
• When the probe is moved on the surface, if a change of resonant frequency is observed, it is due to the
presence of discontinuity only.
• Knowing the frequency at resonance ‘f ’ and velocity of the ultrasonic wave in the test piece ‘v’, the
thickness ‘t’ can be calculated from the relation,
T=v/2f

Video Content / Details of website for further learning (if any):

 http://dx.doi.org/10.6028/NBS.TN.1199
 https://ndt-testing.org/our-services/ultrasonic-testing-pulse-echo-method/
 https://www.google.com/search?q=pulse-
echo+method+pdf&sa=X&ved=2ahUKEwjSm_SUzMfoAhX0wjgGHRaUATQQ1QIoAXoECAw
QAg
Important Books/Journals for further learning including the page nos.:
 G. Sudarmozhi, Engineering Physics, Sri Kandhan publications, 2005, Page no. 2.30-2.35

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LECTURE HANDOUTS L 10

PHYSICS
I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : II Lasers Date of Lecture:

Topic of Lecture: Introduction, Principle of spontaneous emission and stimulated emission.

Introduction :
 Lasers are optical phenomena used in the field of science and technology now a day.
 Laser is an acronym for Light Amplification by Stimulated Emission of Radiation.
 Laser is an extended Maser principle of frequency range 1014Hz-1015Hz in the visible region.
 Due to its remarkable properties, it is used in telecommunications, computers and nuclear reactions and
plays a vital roll in medicine for surgery.
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on properties and propagation of Light
 Basic knowledge in Electronic energy level.
Detailed content of the Lecture:
Characteristics of Lasers
1. Monochromatic
 The laser light is highly monochromatic (having single frequency) than any other light sources.
 The light from the conventional source spreads over wider range of frequencies.
 The line width ∆λ emitted by a laser is nearly 5×10–4 Å but it is only 10–5 for a conventional source.
2. Coherence
 It is an important characteristic of a laser beam. The wave trains are said to be coherent when they are
having same frequency and phase that gives high purity of spectral line.
 Due to this coherence property, it is possible to create high power laser in the order of 1013W of 1μm
diameter.
3. Intensity
 The intensity of laser light is very high.
  1watt laser is many thousand times more intense than 10watt ordinary light.

 Since the beam spread of the laser is very smaller, a narrow beam of light with high energy is
concentrated in a smaller region. This concentration of light beam is expressed in terms of intensity.
4. Directionality
 The ordinary light source emits light in all directions due to spontaneous emission.
 On the other hand, laser emits light only in one direction due to stimulated emissions.
 Ordinary light spreads in all directions with an angular spread of 1m/metre, whereas in laser it is highly
directional with a beam spread of 1mm/metre.
 i.e., laser beam can be focused to very long distance with smaller angular spread.
Spontaneous emission
 An atom in the excited state is returns to ground state by emitting a single photon without any external
inducement.
 The emitted photons move in all directions and are random.
 The radiation of light is less intense, polychromatic and incoherent
 Angular spread is more
Stimulated emission.
 An atom in the excited state is forced to go to ground state, resulting in two photons of same frequency
and energy.
 The emitted photons move in a single direction and are directional.
 The radiation of light is highly intense, monochromatic and coherent
 Angular spread is less
Video Content / Details of website for further learning (if any):
https://spie.org/publications/fg12_p02_spontaneous_and_stimulated_emission?SSO=1
Important Books/Journals for further learning including the page nos.:
Sudarmozhi.G., Engineering Physics I , Bharath Publishers , 2015, Page no.5.2-5.77

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LECTURE HANDOUTS L 11

PHYSICS
I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : II Lasers Date of Lecture:

Topic of Lecture: Population inversion and pumping methods

Introduction :
 Increasing the population of atoms in the higher energy level is essential for laser action.
This can be achieved by the different types of pumping methods. Pumping method is the
transfer of atoms from lower energy level to higher energy level.
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on properties and propagation of Light

Detailed content of the Lecture:

Population inversion
 Consider two energy level systems E1 and E2. Normally the number of atoms (population) presents in
the ground state N1 is higher than the number of atoms in the excited state N2.
i.e., N1 > N2.
 The process of making the number of atoms in the excited state higher than that of the ground state is
called Population inversion (or) Inverted population.
i.e., N2 > N1
 The condition of population inversion is necessary for achieving the stimulated emission of radiation.
Condition for population inversion
 There must be at least a pair of energy levels separated by a desired radiation
 There must be a source to supply energy to the medium
 The atoms must be raised continuously to the exited state
  The process of raising the atoms from ground state to excited state by artificial means is called
Pumping process.
 Optical pumping
 Electric discharge method pumping
 Inelastic collision between atoms
 Direct pumping

Video Content / Details of website for further learning (if any):

https://www.physics-and-radio-electronics.com/ physics/laser/
methodsofachievingpopulationinversion.html

Important Books/Journals for further learning including the page nos.:

Sudarmozhi.G., Engineering Physics I , Bharath Publishers , 2015, Page no.5.7-5.10

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LECTURE HANDOUTS L 12

PHYSICS
I/I

Course Name with Code : Engineering Physics /21BSS01

Course Faculty :
Unit : II Lasers Date of Lecture:

Topic of Lecture: Einstein’s A and B coefficients derivation

Introduction :
Laser makes use of three fundamental phenomena named,
1) Process of absorption
2) Spontaneous emission and
3) Stimulated emission
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on properties and propagation of Light

Detailed content of the Lecture:

1. Process of absorption
i) Number of atoms in the ground state (N1)
ii) Energy density of incident radiation (Q)

Nab = B12N1Q

2. Spontaneous emission
During the downward transition the atoms in the excited energy state return to the ground state
spontaneously by emitting their excess energy ‘h ’ as shown in Fig.4.3. This process is independent
of external radiation and is called spontaneous emission. The rate of spontaneous emission (Nsp) is
depends on the number of atoms in excited state (N2) only.
i.e,
Nsp = A21N2

Where A21 is the probability transition from energy level E2 to E1

3. Stimulated emission
The rate of stimulated emission (N st) is depends on
 i) The number of atoms in the excited state (N2)and
ii) The energy density of incident radiation (Q)

Nst = B21N2Q

Where, B21 is the probability of transition of atoms moving from E 2 to E1 by stimulation. Under
equilibrium condition, the number of upward transitions must be equal to number of downward
transitions.
B12N1Q = A21N2 + B21N2Q
According to Boltzman’s distribution law,
N1
= e (E2 E1 ) kT
= e h kT

N2

A 21 B21
Q =
 B12  h kT
 e 1
 B21 

A21 8 h 3

B21 c3

Video Content / Details of website for further learning (if any):

https://sites.google.com/site/puenggphysics/home/unit-i/relation-between-einstein-s-a-and-b-
coefficient

Important Books/Journals for further learning including the page nos.:

Sudarmozhi.G., Engineering Physics I , Bharath Publishers , 2015, Page no.5.3-5.6

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LECTURE HANDOUTS L 13

PHYSICS
I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : II Lasers Date of Lecture:

Topic of Lecture: Types of lasers - He-Ne laser

Introduction :
 In the mixture of helium and neon gases, He atoms are excited by electric discharge
method.
 Excited He atoms collides with Ne atoms and raised it to higher energy level.

Prerequisite knowledge for Complete understanding and learning of Topic:

 Basic knowledge on properties and propagation of Light

Detailed content of the Lecture:

 Consist of gas discharge tube made of quarts with 80 cm long and 1.5 cm width.
 The discharge tube is filled with themixture of neon at 0.1mm of mercury pressure and He at 1
mm of mercury pressure as active medium.
 The ratio of He-Ne mixture is 10:1
 He has the majority and Ne has the minority atoms
  The excited helium atoms transfer their energy to the neon atoms in the ground state by
resonance collision method.
 Ne atoms are raised to the excited state E4 and E6
 When the population of the neon atoms in the energy level f4 and f6 becomes dominant, the
stimulated emission starts.
 Release of laser of wavelength (E6 → E3) 6328
 E6 → E5: 3.29

Video Content / Details of website for further learning (if any):

https://www.physics-and-radio-electronics.com/ physics/laser/
methodsofachievingpopulationinversion.html

Important Books/Journals for further learning including the page nos.:

Sudarmozhi.G., Engineering Physics I , Bharath Publishers , 2015, Page no.5.15-5.19

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LECTURE HANDOUTS L 14

PHYSICS
I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : II Lasers Date of Lecture:

Topic of Lecture: Nd-YAG laser

Introduction :
Yittrium Aluminum Garnet crystal doped with Neodymium is used as an active medium. The
neodymium ions are excited to higher energy level by optical pumping and fall back to metastable state
spontaneously. During the downward transition from metastable state to ground state, laser is emitted by
stimulation.
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on properties and propagation of Light

Detailed content of the Lecture:

Construction
It is a four level doped insulator laser. Nd–YAG crystal is an active medium in which few of the
Yittrium ions are replaced by Neodymium ions. The length of the crystalline rod varies from 5-10cm
and diameter varies from 6-9mm. Nd–YAG crystalline rod along with the source say xenon or krypton
lamp is placed inside a highly elliptical reflector cavity.

This makes the entire radiation from flash lamp to focus on Nd–YAG rod. The optical resonator
is formed by using two reflecting plates highly polished and parallel in which one is fully reflecting and
the other is partially reflecting.

 Working
The flash lamp is switched on and the light is allowed to fall on the rod. The neodymium atoms
are pumped to higher energy levels E 2 and E3 from E1 as shown in Fig 4.7. From these higher excited
energy levels, the atoms make non radiative transitions to metastable state E4 and then the population
inversion is achieved (i.e, E4 becomes more populated) within few milliseconds. Then the stimulation
starts and the stimulated emission is dominating between the energy levels E 4 and E5.
These stimulated photons undergo multiple reflections between the parallel plates and the energy
increases abruptly. After reaching sufficient energy the laser beam is emerging out of partially reflecting
plate with a wave length of 1.06μm.

Video Content / Details of website for further learning (if any):

https://www.physics-and-radio-electronics.com/ physics/laser/
methodsofachievingpopulationinversion.html

Important Books/Journals for further learning including the page nos.:

Sudarmozhi.G., Engineering Physics I , Bharath Publishers , 2015, Page no.5.13-5.15

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LECTURE HANDOUTS L 15

PHYSICS
I/I

Course Name with Code : Engineering Physics /21BSS01

Course Faculty :
Unit : II Lasers Date of Lecture:

Topic of Lecture: Semiconductor lasers (homojunction & heterojunction)

Introduction :
A p-n junction made of same material with two different conducting regions say n-type and p-
type is called as homojunction. The homojunction devices are lacking in carrier containment and
hence, it is an insufficient light source. The devices like LED are fabricated with homojunction diode
laser.

Prerequisite knowledge for Complete understanding and learning of Topic:

 Basic knowledge on properties and propagation of Light

Detailed content of the Lecture:

4.7.3.1 Homojunction Semiconductor laser

A p-n junction made of same material with two different conducting regions say n-type and p-
type is called as homojunction. The homojunction devices are lacking in carrier containment and
hence, it is an insufficient light source. The devices like LED are fabricated with homojunction diode
laser.
 Principle
When p-n junction is forward biased, the holes are moving towards ‘n’ region and electrons are
moving towards ‘p’ region. The recombination of charge carrier takes place in the junction region
which results laser radiation.
It is most compact of all lasers and also called injection laser. The p-n junction
diode of a single crystalline material (Eg: Gallium arsenide) is acts as an active medium. Gallium
arsenide is a direct band gap semiconductor used for laser action. The indirect band gap
semiconductors namely silicon and germanium are not used for laser action. The p and n regions of
gallium arsenide is highly doped with holes and electrons respectively.
 The thickness of junction layer is very narrow so that radiation has large divergence. The faces
of p and n regions at the junction region are made parallel and well polished. This plays a roll of optical
resonator. The upper and lower electrodes connected with p and n regions helps for the supply of
current to the diode.
 Working
The population inversion is achieved by injecting the charge carriers across the junction region
by forward biasing. For direct recombination process, the current in the order of 10 4 ampere/cm2 is
passed through the electrodes. The photons are emitted during recombination of electrons and holes
and the rate of recombination increases. The emitted photons from recombination process are having
the same phase and frequency as that of original inducing photons and will be amplified to get a beam
of laser.

Video Content / Details of website for further learning (if any):

https://www.physics-and-radio-electronics.com/ physics/laser/
methodsofachievingpopulationinversion.html

Important Books/Journals for further learning including the page nos.:

Sudarmozhi.G., Engineering Physics I , Bharath Publishers , 2015, Page no.5.19-5.24

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LECTURE HANDOUTS L 16

PHYSICS
I/I
Course Name with Code : Engineering Physics / 21BSS01
Course Faculty :
Unit : II Lasers Date of Lecture:

Topic of Lecture: Industrial Applications - Lasers in welding, cutting, heat treatment

Introduction :
 laser beams are widely used in many fields of science, engineering and medicine.

Prerequisite knowledge for Complete understanding and learning of Topic:

 Basic knowledge on properties and propagation of Light
Detailed content of the Lecture:
 Laser in welding
High power lasers are generally used for laser welding and cutting. In an ordinary welding
process heat is induced on the area being welded, so that the material in that area will go to molten
state. The heat will spread all over the surrounding and hence it damages the material. While using
the laser, due to high directionality, it is concentrated at the particular area without affecting its
surrounding.
The metal plates to be welded are in contact at their edges and the laser beam is made to
move along the line of contact. This high directional, concentrated laser beam heats the edges of the
plate and melts, which causes the plate to fuse together.
 Lasers in cutting and drilling
Powerful lasers are required for cutting the materials. The power required is depending on the
material being cut. The energy must be supplied in such a way that rapid evaporation of material
takes place without diffusion of heat into work piece.
 Laser heat treatment
This kind of treatment is used for altering the compositions and microstructure of surface
layers and thereby improving the surface hardness.
The powerful laser beam is made to fall on the surface of the material. The portion which is
exposed to the laser beam gets heated. When the beam is moved over the surface of the material the
heated spot cools down rapidly. While moving the laser over entire surface of the material the
strength of the material is enhanced by the method called quenching.
 Medical applications
 Laser is widely used in surgery in the treatment of detached retina
 It finds applications in bloodless micro surgery
 Lasers in microelectronics
Microelectronics is related to the study and manufacture of very small electronic components.
These devices are made from semiconductors with the help of lasers using a process called
photolithography. Laser is used in the fabrication process of microelectronic component due to its
unique characteristics.
 Industrial applications
 Lasers are used in material processing
 Lasers are used in printing and jewelry industry
 Communication and engineering applications
 Lasers have wider applications in connection with optical fiber

Video Content / Details of website for further learning (if any):

https://www.physics-and-radio-electronics.com/ physics/laser/
methodsofachievingpopulationinversion.html

Important Books/Journals for further learning including the page nos.:

Sudarmozhi.G., Engineering Physics I , Bharath Publishers , 2015, Page no.5.25-5.28

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LECTURE HANDOUTS L 17

PHYSICS
I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : II Lasers Date of Lecture:

Topic of Lecture: Medical applications of lasers

Introduction :
 laser beams are widely used in many fields of science, engineering and medicine.

Prerequisite knowledge for Complete understanding and learning of Topic:

 Basic knowledge on properties and propagation of Light

Detailed content of the Lecture:

. Medical applications
 Laser is widely used in surgery in the treatment of detached retina
 It finds applications in bloodless micro surgery
 Lasers are used in cancer treatment and in the treatment of brain tumors
 The availability of optic fibers permitted the combination of laser technology with endoscop
Video Content / Details of website for further learning (if any):
https://www.physics-and-radio-electronics.com/ physics/laser/
methodsofachievingpopulationinversion.html

Important Books/Journals for further learning including the page nos.: 5.27

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LECTURE HANDOUTS L 18

PHYSICS
I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : II Lasers Date of Lecture:

Topic of Lecture: Holography (construction & reconstruction)

Introduction :
 The hologram acts as a diffraction grating and secondary waves from hologram interferes
constructively in certain directions and destructively in other directions. They form a real image in
front of the hologram and a virtual image behind the hologram at the original site of the object.
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on properties and propagation of Light

Detailed content of the Lecture:

 construction of image(freezing)
A weak but broad beam of laser light is splitted into wo beams by means of beam splitter. One beam
directly goes to the photographic film is called as reference beam and second beam illuminates the
object called as object beam. The light scattered by the object moves towards the photographic plate
and interferes with the reference beam. The photographic plate carrying complex interference pattern
of the object is called hologram.

 .Reconstruction (unfreezing): A laser beam identical to the reference beam is used for
reconstruction of the object. This read out bream illuminates the hologram at the same angle as
the reference beam. The hologram acts as a diffraction grating and secondary waves from
hologram interferes constructively in certain directions and destructively in other directions.
They form a real image in front of the hologram and a virtual image behind the hologram at the
 original site of the object. An observer sees light waves diverging from the virtual image. An
image of the object appears where the object once stood and the image is identical to what our
eyes would have perceived in all its details of the object.

Application:
 Hologram is reliable medium for data storage
 Hologram is used in concerts
 Hologram are used for authentication
 Holograms are used in exhibitions to avoid possible thefts.

Video Content / Details of website for further learning (if any):

https://www.physics-and-radio-electronics.com/ physics/laser/
methodsofachievingpopulationinversion.html

Important Books/Journals for further learning including the page nos.:

Sudarmozhi.G., Engineering Physics I , Bharath Publishers , 2015, Page no.5.29-5.30

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LECTURE HANDOUTS L 19

PHYSICS
I/I

Course Name with Code : ENGINEERING PHYSICS /21BSS01

Course Faculty : Date of Lecture:

Unit : III - FIBER OPTICS AND ITS APPLICATIONS

Topic of Lecture: Introduction and Principle of Fiber optics

Introduction :
 Optical fibers are the light pipes or photon conductors made of transparent materials like glass and
plastics. The development of lasers and optical fibers has brought a revolution in communication
systems.

Prerequisite knowledge for Complete understanding and learning of Topic:

 To know the basic knowledge about the principle of Fiber optics.
 To know the definition of fiber optics “Fibre optics is a technology in which the electrical signals are
converted into light signals, transmitted through a glass fibre and reconverted into electrical signals”.

Detailed content of the Lecture:

. FIBRE OPTICS - INTRODUCTION
To have an efficient communication system, the information carried out by light waves requires
a guiding medium through which it can be transmitted safely. This guiding medium is called optical
fiber. Apart from the use of communication, optical fibres are widely used in other areas like medical
diagnosis and sensors for detecting electrical, mechanical and thermal energies.
CONSTRUCTION OF THE OPTICAL FIBRE
An optical fibre is a transparent media as thin as human hair, made of glass or plastic used to
guide the light waves along its length. An optical fibre works on the principle of total internal
reflection. When the light enters at one end of the fibre it undergoes total internal reflection from the
side walls and travel the length of the fibre.
 Light transmission through fiber
Optical fibre is constructed with three coaxial regions .The inner cylinder made of glass or
plastic called core is used to guide the light. It is surrounded by a middle region of glass or plastic
called cladding which is used to confine the light to the core.
The cladding is covered by the outermost region called buffer, which protects the inner region
from the moisture. The refractive index of core region is always higher than the cladding.

Structure of fiber

Light entering the core and striking the core-cladding interface at an angle greater than critical
angle will be reflected back into the core. The light beams undergo total internal reflection and passes
along the length of the cable. Since the angle of incidence and reflection are equal, the light will
continue to propagate through the fibre.

PRINCIPLE OF FIBER TRANSMISSION

The principle of transmission of light through optical fiber is total internal reflection. For total
internal reflection, the angle of incidence (θ i) should be greater than the critical angle (θc) of the
medium.

a ) when θi < θc b) when θi = θc c) when θi > θc

Principle of total internal reflection
Case 1: When θi < θc, the light ray is refracted into the rarer medium (cladding) i.e., no light is
transmitted through the core region, as shown in Fig.a.
Case 2: When θi = θc, the angle of incidence is increased to a certain value called critical angle so
that angle of refraction is 90º. The refracted ray just emerges along the core-cladding interface
as shown in Fig.b.

Case 3: When θi > θc, the light is reflected back into the denser medium (core). In order to arrive at the
condition of total internal reflection, the angle of incidence must be higher than the critical
angle. The reflection of light in the core region is shown in Fig.c.
Video Content / Details of website for further learning (if any):
https://en.wikipedia.org/wiki/Optical_fiber
http://www.jb.man.ac.uk/research/fibre/intro2fibre.htm

Important Books/Journals for further learning including the page nos.:

Engineering Physics, Dr.G.SudarMozhi, Sri kandhan Publication,2016. Page No.4.1-4.4

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LECTURE HANDOUTS L 20

PHYSICS
I/I

Course Name with Code : ENGINEERING PHYSICS /21BSS01

Course Faculty : Date of Lecture:

Unit : III - FIBER OPTICS AND ITS APPLICATIONS

Topic of Lecture: Propagation of light in optical fibers Numerical aperture and Acceptance angle

Introduction :
 Numerical aperture -In optics, the numerical aperture (NA) of an optical system is a dimensionless
number that characterizes the range of angles over which the system can accept or emit light.
 Acceptance angle-The acceptance angle of an optical fiber is defined based on a purely geometrical
consideration (ray optics): it is the maximum angle of a ray (against the fiber axis) hitting the fiber core
which allows the incident light to be guided by the core.

Prerequisite knowledge for Complete understanding and learning of Topic:

 Basic knowledge about the refractive index of core and cladding

Detailed content of the Lecture:

PROPAGATION OF LIGHT IN OPTICAL FIBERS
Let us consider the optical fibre into which light is entered at one end . Let n1 is the refractive index
of core and n2 is the refractive index of cladding. The refractive index of the core is always greater than
the refractive index of cladding i.e., n1 > n2.
Let n0 is the refractive index of the medium (air) where the light is entering into the fibre. The
light is allowed to travel along the path OA and enters into the core at an angle of θi to the axis of fibre.
The light is refracted at an angle of θr and strikes the core-cladding interface at an angle of φ at B. If 
is greater than the critical angle θc, the ray undergoes total internal reflection and propagates through
the fiber.
 Light propagation in optical fiber

According to Snell’s law,

n0 sin θi = n1 sin θr ---------- (1)

At B, on the interface of core-cladding,

 = 90 – θr

Applying Snell’s law again,

n1sin (90 – θr) = n2 sin 90

n1cosθr=n2  sin(90–θr)=cosθrand
sin 90 = 1

n2
cos θr = ------- (2)
n1

Rewriting equation (1),

n1
sin θi = sin θr
n0

n1
= 1  cos2  r ---------- (3) sin2θ + cos2θ = 1
n0

Substituting the value of cos θr in equation (3) from equation (2), sin2θ = 1– cos2θ

n n2 2
sin θi = 1 1 2 sin θ = 1 cos 2 
n0 n1

n1 n12  n2 2
=
n0 n12

n12  n2 2
=
n0

n12  n2 2
θi = sin–1 ---------- (4)
n0
Equation (4) is called Acceptance angle (θi), the maximum angle at which a ray of light can enter
through the fibre so that the light will be totally internally reflected.
Numerical aperture

It is the measure of amount of light rays that can be accepted by the fibre. The sine of the acceptance
angle of the fibre is called numerical aperture.

n12  n2 2
i.e, NA =
n0

When the medium surrounding the fibre is air, n0 = 1

NA = n12  n2 2

Fractional index change (  )

It is the ratio of difference in refractive index of core and cladding to the refractive index of core.
n1  n2
i.e.,  = -------- (5)
n1

Relation between Numerical aperture (NA) and Fractional index change (  )

From equation (5), we can write
n1  = n1 – n2. --------- (6)

We know, NA = n12  n2 2

= (n1  n2 )(n1  n2 ) ---------- (7)

Substituting the equation (6) in (7),

NA = (n1  n2 )(n1)

If n1  n2 ,

NA = 2n12  - ----- (8)

NA = n1 2

Video Content / Details of website for further learning (if any):

https://circuitglobe.com/numerical-aperture-of-optical-fiber.html
https://vlab.amrita.edu/?sub=1&brch=189&sim=343&cnt=1

Important Books/Journals for further learning including the page nos.:

Engineering Physics, Dr.G.SudarMozhi, Sri kandhan Publication, 2016. Page No.4.4 - 4.7

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LECTURE HANDOUTS L 21

PHYSICS
I/I

Course Name with Code : ENGINEERING PHYSICS /21BSS01

Course Faculty : Date of Lecture:

Unit : III - FIBER OPTICS AND ITS APPLICATIONS

Topic of Lecture: Classification based on materials and refractive index profile

Introduction :

Fiber Classifications. Optical fiber falls into three basic classifications: step-index multimode, graded-
index multimode, and single mode. A mode is essentially a path that light can follow down the fiber.
Step-index fiber has a core with one index of refraction, and a cladding with a second index
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic definition of refractive index
 Core and Cladding

Detailed content of the Lecture:

Optical fibers are generally classified based on refractive index profile, modes of

propagation
Optical fiber based on refractive index profile
Based on the refractive index of core and cladding materials, fibres are classified into
i) Step index fibre and
ii) Graded index fibre
i) Step index fibre
If the refractive index of the core is uniform throughout and undergoes a change only at
cladding boundary is called step index fibre. As the refractive index of core (n1) and cladding (n2) is
changed step by step, it is called step index fibre. The light ray is propagated in the form of meridinal
rays and it passes through the axis of the fibre.
 Step index fiber

ii) Graded index fibre

If the refractive index of the core is varying with the radial distance from the axis of the fibre it
is called graded index fibre. The refractive index is maximum at the axis of the core and goes on
decreasing while moving towards core-cladding interface i.e., the refractive index of core and cladding
are equal, at the core-cladding interface. The light ray is propagated in the form of skew rays and it will
not cross the axis of the fiber.

Graded index fiber

Difference between step index fibre and graded index fiber:

S.No Step index fibre Graded index fibre

1 The refractive index of core (n1) and The refractive index of the core is varying
cladding (n2) is changed step by with the radial distance from the axis of the
step, it is called step index fibre fibre it is called graded index fibre
2 The light ray is propagated in the The light ray is propagated in the form of
form of meridinal rays and it passes skew rays and it will not cross the axis of
through the axis of the fibre. the fibre
3 It has lower bandwidth It has higher bandwidth
4 Distortion is more Distortion is lesser
Video Content / Details of website for further learning (if any):
https://en.wikipedia.org/wiki/Refractive_index_profile
http://msheiksirajuddeen.blogspot.com/2011/12/optical-fibres-are-generally-classified.html

Important Books/Journals for further learning including the page nos.:

Engineering Physics, Dr.G.SudarMozhi, Sri kandhan Publication,2016. Page No.4.7-4.9

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LECTURE HANDOUTS L 22

PHYSICS
I/I

Course Name with Code : ENGINEERING PHYSICS /21BSS01

Course Faculty : Date of Lecture:

Unit : III - FIBER OPTICS AND ITS APPLICATIONS

Topic of Lecture: Classification based on materials, refractive index profile

Introduction :
 Single mode fiber
 Multimode fiber
 Glass fibre
 Plastic fibre

Prerequisite knowledge for Complete understanding and learning of Topic:

 Basic knowledge about the optical fibre

Detailed content of the Lecture:

Optical fiber based on modes of propagation
Based on the modes of propagation, optical fibres can be further classified into
i) Single mode fibre and
ii) Multimode fibre.
i) Single mode fibre
Single mode fibre is the fiber in which light travels along a single path that is along the axis.
This type of fibre may have a core diameter of 2–10μm and cladding diameter of 50–125μm. Due to its
small core diameter, a single mode of light transmission is only possible. This is used for long distance
communication. Laser beam can be easily launched into this single mode fibre.

Single mode step index fibre

The advantages of single mode step index fibre are stated below.
 It has very small core diameter
  Since it allows only one mode, the entire light energy is concentrated along the axis
 They provide superior transmission quality
 Transmission loss is very small
 It is compatible with integrated optic technology
 Life time of more than 20years is anticipated
ii) Multi mode fibre
A multimode optic fibre is one in which more than one path is possible for light rays to travel
through the core. A typical multimode optical fibre has a core diameter in the range of 50-200μm. The
light can be launched into multimode fibre using LED.
The disadvantage of multimode fibre is that they suffer from intermodel dispersion. Multimode
propagation can be achieved in both step index and the graded index fibres and is explained below.
A multimode step index fibre is similar to the single mode step index fiber with large core
diameter. The light travels in zigzag path inside the fibre and many such paths of propagation are
permitted. Each path of light is travel with slightly different velocities.

Multimode step index fibre

A multimode graded index fibre has a core diameter of 50-200μm and cladding diameter of
100-250μm. The refractive index of the core is maximum at the axis of the fibre. If the diameter of the
core is high, the intermodal dispersion loss must be high. But because of gradual decrease in the
refractive index of the core, the intermodal dispersion loss is minimized. The propagation of light in
this type of fibre.

Multimode graded index fibre

Optical fibers based on materials
. Based on the materials used for the manufacturing of optical fibre, they are classified into
i) Glass fibre and
ii) Plastic fibre
i) Glass fibre

The glass fibres are prepared by fusing the mixture of metal oxides and silica glasses. Silica
(SiO2) having refractive index of 1.458 is commonly used for glass fibres. To produce the materials
having slightly different refractive indices for core and cladding, some of the dopants will be added to
silica. Refractive index of silica increases with the addition of GeO 2 or P2O5 and decreases with the
addition of B2O3. The resulting material is randomly connected by molecular network rather than well
defined ordered structures as found in crystalline materials.

Some of the fibre compositions are;

 1. GeO2–SiO2 as a core and SiO2 as a cladding

2. P2O5–SiO2 as a core and SiO2 as a cladding

3. SiO2 as a core and B2O3–SiO2 as a cladding

ii) Plastic fibre

Plastic fibres are made of plastics. It is of low cost. It has higher signal attenuation than glass
fibres. It can be handled without any special care due to its toughness and durability. Since refractive
index differences between core and cladding is higher, numerical aperture and angle of acceptance of
this type of fibre is also higher.

Some of its compositions are,

1. Polystyrene as core and methylmetha crylate as cladding
2. Methylmetha crylate as core and its co-polymer as cladding
FIBER MATERIALS
The materials used for fabricating optical fibres must satisfy the following conditions:

1. It must be possible to make long, thin and flexible fibres from the materials

2. It must be transparent to guide the light efficiently

3. Materials having slightly different refractive indices for the core and cladding must be
available

4. The material must be available at low cost with higher efficiency

Video Content / Details of website for further learning (if any):
http://msheiksirajuddeen.blogspot.com/2011/12/optical-fibres-are-generally-classified.html

Important Books/Journals for further learning including the page nos.:

Engineering Physics, Dr.G.SudarMozhi, Sri kandhan Publication,2016. Page No.4.9-4.12

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`
LECTURE HANDOUTS L 23

PHYSICS
I/I

Course Name with Code : ENGINEERING PHYSICS /21BSS01

Course Faculty : Date of Lecture:

Unit : III - FIBER OPTICS AND ITS APPLICATIONS

Topic of Lecture: Double crucible technique of fibre and Splicing

Introduction :
In Double Crucible technique
 Fabrication cost is low
 Fibres can be fabricated continuously
In Splicing


Splicing is a method used to connect the fibres permanently to carry the information for a longer
distance
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge about the fiber.
 Principle of Fiber Optics

Detailed content of the Lecture:

. FABRICATION OF GLASS FIBRE - Double Crucible Technique
Principle
The raw materials of core and cladding are separately placed in the crucibles (a pot in which
substances are heated to higher temperatures) kept one inside the other and is heated to very high
temperature using a furnace. The molten materials are drawn out together to form the fibre.
Description
The experiment consists of two crucibles namely inner and outer crucibles made of platinum or
silica. The inner crucible is kept inside the outer crucible. The inner crucible contains core glass and
the outer crucible contains the cladding glass materials. Both the crucibles are placed inside a vertical
furnace, which is capable of heating up to 1200ºC. Using this technique, various refractive indices of
core and cladding is obtained by adding the dopant materials.
 Double Crucible Technique
Working
Highly purified molten materials of different refractive indices are taken into inner and outer
crucibles. The core glass powder is taken in inner crucible and cladding glass powder is taken in outer
crucible. The electric furnace is switched on and materials inside the crucibles are heated to the higher
temperature and melted. Then the molten material is allowed to emerge out through the nozzle of the
crucible. Now the core material will start diffusing into the cladding material to form an optical fibre
and fibre is drawn out through the bottom of the outer crucible. Finally the fibre is coated by the
polymer and protective layers.
Advantages
 Fabrication cost is low
 Fibres can be fabricated continuously
Disadvantages
 Materials used for core and cladding should be pure, otherwise contamination will occur
 Silica crucibles should not be used more than once, in such cases crucibles made of platinum
should be used, which is costlier
SPLICING OF FIBRE
Splicing is a method used to connect the fibres permanently to carry the information for a
longer distance. In this technique two fibres can be connected with the help of an elastomer (rubber)
and adhesive gel.
There are two types of splicing technique namely,
1) Fusion splicing
2) Mechanical splicing
Fusion splicing
In this splicing, the two fibre ends are viewed through a microscope and then aligned. An
electric arc consists of tungsten electrodes are used as heating source for fusion. After the alignment,
the electric arc emits a spark between electrodes at the gap to burn off dust and moisture. The spark
raises temperature above the melting point of the glass and fusing the ends together permanently.
 Fusion splicing
Mechanical splicing
Mechanical splicing is preferred for the short and medium routes. It provides greater flexibility.
The mechanical mounts are used to hold the fibres in position. Any kind of irregularities like scratches
while cleaning the fibre ends will lead a loss of optic power.

Mechanical splicing
The matching gel is injected in the region where the ends of two fibres are kept. The matching
gel is a highly transparent semi fluid with an index matching the refractive index of the core. The light
energy which emerges out of one end of fibre is flowing freely through the matching gel and reaching
another fibre. Thus the optical energy is transferred from one fibre to another.
Video Content / Details of website for further learning (if any):
https://www.youtube.com/watch?v=-MqnnTk2LB0
https://www.brainkart.com/article/Double-Crucible-Method_6892/
https://en.wikipedia.org/wiki/Fusion_splicing
Important Books/Journals for further learning including the page nos.:
Engineering Physics, Dr.G.SudarMozhi, Sri kandhan Publication,2016. Page No.4.13-4.16

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LECTURE HANDOUTS L 24

PHYSICS
I/I

Course Name with Code : ENGINEERING PHYSICS /21BSS01

Course Faculty : Date of Lecture:

Unit : III - FIBER OPTICS AND ITS APPLICATIONS

Topic of Lecture: Loss in optical fiber – attenuation, dispersion, bending

Introduction :
The loss of transmission causes in the fibre is due to
 Attenuation
 Dispersion
Prerequisite knowledge for Complete understanding and learning of Topic:
 To know the basics knowledge about transmission, dispersion and absorption

Detailed content of the Lecture:

. LOSS IN OPTICAL FIBRE
When the light is transmitted through the optical fibre it suffers transmission losses. The loss of
transmission causes in the fibre is due to
1) Attenuation 2) Dispersion
Attenuation
Loss of optical power by the optical signal in the fibre is called attenuation. Attenuation is also
defined as the ratio of the output power (Pout) of a fibre of length L, to the input power (Pin).
10 P 
Attenuation = log  out  in dB/km
L  Pin 
The attenuation may be explained with respect the following factors:
i) Absorption due to impurity ions
ii) Rayleigh scattering due to inhomogeneties and
iii) Radiative loss by wave guide imperfection and micro bending.
i) Absorption
Absorption is related to the materials used for fibre and is caused by,
a) atomic defects
b) extrinsic absorption
 c) intrinsic absorption
a) Atomic defects: Atomic defects are the imperfections of the atomic structure of fibre
material such as missing molecules and high density clusters of atoms. The losses arises from these
defects are negligible compared to intrinsic and extrinsic effect.
b) Extrinsic absorption: The presence of impurity plays a vital role in the absorption process.
When the light waves are transmitted through fibre materials, some of the photons are absorbed by
these impurities and some of the photons interact with these impurities. The electrons of the impurity
atoms absorb the photons and get excited to higher energy level. Later these electrons give up their
absorbed energy in the form of heat energy or light energy. This leads some loss of energy.
c) Intrinsic absorption: The property of absorbing light energy by the fibre material even it is
free from impurities and defects is called intrinsic absorption.
ii) Scattering loss
We know the glass materials are used for the fabrication of fibres. By nature glass has a
disordered structure in which the material density fluctuations are absorbed in the composition. This
leads the variation of refractive index of the glass. The variation of refractive index of the material
causes the light scattered called Reyleigh scattering.
Due to scattering, the photon moves in random direction and having the probability of leaving
the fibre thus leads a loss of energy.
iii) Radiative loss
Radiative loss occurs in fibre due to bending of radius of curvature. The bending of fibre may
be classified into
a) Microscopic bending and b) Macroscopic bending.
a) Microscopic bending
These kinds of losses are due to non-uniformity or micro bends inside the fibre material.

Microscopic bending loss

These micro bending are also caused due to non-uniform pressure created during the cabling of
fibre or during manufacturing. The lights which get reflected from these surfaces are escaped from the
fibre material and leads loss of energy.
Micro bending losses can be reduced by providing a compressible jacket over the fibre which
protects the core region.
b) Macroscopic bending
 In which the radius of the core is large compared to fibre diameter. This kind of bending is
occurred when a fibre cable turns at a corner. At these corners the light will not satisfy the condition
for total internal reflection and hence it escapes from the fiber. It causes large curvature radiation
losses.
Dispersion
The degradation of the optical signal when the light travels along a fibre is called dispersion.
The most significant types of dispersion in fibre optic cable are,
i) Chromatic dispersion ii) Modal dispersion iii) Waveguide dispersion
i) Chromatic dispersion This type of dispersion is occurred due to different wavelength of light
traveling at different speed inside the fibre. The effect of chromatic dispersion can seen when a white
light passes through a glass prism and is spread out into the colours.
Chromatic dispersion can be reduced by improving the quality of the light source and by
increasing the purity of the glass material.
ii) Modal dispersion When more than one mode is propagating through a fibre the modal dispersion
occurs. Some modes of light travel slow and some other modes of light travel faster. The light pulses
arrive at the fibre end at slightly different time will cause the pulse to spread out in time as it travels
along the fibre. This effect is known as intermodal dispersion.
Modal dispersion can be reduced by improving the quality of light source.
iii) Waveguide dispersion
This dispersion is caused by the shape of the fibre core and by its chemical composition. The
light dispersed while traveling through the fibre cable can be controlled by modifying the composition
of glass.
Video Content / Details of website for further learning (if any):
https://www.fiberoptics4sale.com/blogs/archive-posts/95048006-optical-fiber-loss-and-attenuation
https://www.juniper.net/documentation/en_US/release-independent/junos/topics/concept/fiber-optic-
cable-signal-loss-attenuation-dispersion-understanding.html
Important Books/Journals for further learning including the page nos.:
Engineering Physics, Dr.G.SudarMozhi, Sri kandhan Publication,2016. Page No.4.16-4.20

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Rasipuram - 637 408, Namakkal Dist., Tamil Nadu

LECTURE HANDOUTS L 25

PHYSICS
I/I

Course Name with Code : ENGINEERING PHYSICS /21BSS01

Course Faculty : Date of Lecture:

Unit : III - FIBER OPTICS AND ITS APPLICATIONS

Topic of Lecture: Fibre optical communication system

Introduction : The basic concept of optical fiber communication is similar to other types of
communication system. In the fiber optic communication system, initially the input electrical signals
are converted into optical signals by a transmitter.

Prerequisite knowledge for Complete understanding and learning of Topic:
i) Transmitter
ii) Optical fibre
 iii) Receiver
Detailed content of the Lecture:
. FIBER OPTIC COMMUNICATION SYSTEM
The basic concept of optical fiber communication is similar to other types of communication
system. In the fiber optic communication system, initially the input electrical signals are converted into
optical signals by a transmitter. Then the signals are allowed to transmit through optical fibre without
any loss of energy. The light signals are received at the end of the fiber then converted into electrical
signals by a receiver.
The basic components of fibre optic communication systems are,
i) Transmitter
ii) Optical fibre
iii) Receiver
Transmitter
The transmitter consists of a light source supported by necessary drive circuits. The source is
the active component in optical communication system. The information signal source which is in the
analog form to be transmitted is converted from analog signal to electrical signal. This results in
successful launching of light into the optical fiber. The drive circuit transfers the electric input signal
into digital pulses and it is converted into optical pulses by the light source. The light source is
generally a LED. The optical pulses are focused onto the optical fibre.

Fibre optic communication system

Optical Fibre
It acts as a wave guide and transmits the optical pulses towards the receiver by the principle of
total internal reflection. The transmission medium may be either wires or coaxial cables.
Receiver
Similar to the source, detector is an important component in fiber optic communication system.
The photo detector receives the optical pulses and converts the optical pulses into electrical pulses. The
electrical signals are amplified by an amplifier. These electrical signals are converted from digital to
analog signals and reach the receiver end.
Video Content / Details of website for further learning (if any):
https://en.wikipedia.org/wiki/Fiber-optic_communication
https://www.elprocus.com/basic-elements-of-fiber-optic-communication-system-and-its-
working/
Important Books/Journals for further learning including the page nos.:
Engineering Physics, Dr.G.SudarMozhi, Sri kandhan Publication,2016. Page No.4.20-4.22

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LECTURE HANDOUTS L 26

PHYSICS
I/I

Course Name with Code : ENGINEERING PHYSICS /21BSS01

Course Faculty : Date of Lecture:

Unit : III - FIBER OPTICS AND ITS APPLICATIONS

Topic of Lecture: Fiber optic Light sources

Introduction :
 Light Emitting Diode
 Semiconductor laser diode
Prerequisite knowledge for Complete understanding and learning of Topic:
 To Know the basic knowledge about the Light Emitting Diode and Semiconductor laser diode

Detailed content of the Lecture:

LIGHT SOURCES FOR FIBRE OPTICS
Light Emitting Diode (LED)
LED is a semiconductor p-n junction diode which converts electrical energy into light energy
under forward bias condition. It emits light in both visible and infrared region.
Principle
The principle used in the LED is injection luminescence. When LED is forward biased, the
majority of positive charge carriers moves from ‘p’ to ‘n’ region and negative charge carriers moves
from ‘n’ to ‘p’ region and becomes excess minority carriers. This excess minority charge carriers
diffuses through the junction and recombines with the majority charge carriers in n and p region
respectively.
Construction
The p-n junction is made by doping Silicon with GaAs crystal using diffusion or epitaxial
techniques. A shallow p-n junction is formed on GaAs substrate such that ‘p’ layer is formed by
diffusion on ‘n’ layer. The thickness of ‘n’ layer is taken higher than that of ‘p’ layer, to increase the
probability of charge carriers to recombine.
 Light Emitting Diode
Ohmic contacts are made with the help of aluminium in such a way that top layer of the ‘p’
material is left uncovered for the emission of light. Biasing is done using ohmic contacts. The whole p-
n junction is insulated to minimize the losses due to reflection.
Working
When the diode is forward biased, the majority charge carriers from ‘n’ and ‘p’ region cross the
junction and become minority charge carriers in the other region. i.e., the majority of electrons in ‘n’
region cross the junction and reach the ‘p’ region and become minority charge carriers in ‘p’ region.
Like wise the majority of holes in ‘p’ region cross the junction and reach the ‘n’ region and become the
minority charge carriers in the ‘n’ region. The excess of minority carriers are injected in both ‘p’ and
‘n’ region.

Recombination of charge carriers

Similarly the excess minority carriers of holes in n region recombine with the electrons which are the
majority carriers in n region and then laser radiates.
Thus the electron hole recombination process occurs more and more and the light energy is
emitted through the top layer of ‘p’ material as shown.
Advantages
 They are smaller in size.
 The cost of diode is very low.
 .
Disadvantages
 Power output is very low.
 Intensity is lesser.
 .
Semiconductor Laser Diode
Principle
The electrons in conduction band combines with a holes in the valence band and hence the
recombination of electron and hole produces energy in the form of light.
Construction
 This kind of diode is a combination of different layers. It consists of five layers. A layer of p
type semiconductor (Layer-3) made of GaAs will acts as an active region. This semiconductor layer
has a narrow band gap. This layer is placed between two layers (Layer-2 and 4) having wider band gap.
The p type layer of GaAs
(Layer-1) is used for making necessary biasing with the lower electrode. All the four layers are grown
over the substrate (Layer-5) which is made of n type of GaAs. The junction between the 3 rd and 4th
layer is well polished and hence it acts as an optical resonator.

Semiconductor Laser Diode

Working
The Diode is forward biased with the help of electrodes. Due to forward biasing the charge
carriers are produced in the layers 2 and 4. The charge carriers produced are injected into the active
region (Layer-3) till the population inversion is achieved. Some of the spontaneously emitted photons
released during recombination process start stimulate the injected charge carriers to emit photons. After
the condition of population inversion is reached more number of photons are produced. The photons
are reflected back and forth and hence the intense coherent beam of laser emerges out from the p- n
junction region between the layers 3 and 4.

Video Content / Details of website for further learning (if any):

https://circuitglobe.com/light-emitting-diode-led.html
https://en.wikipedia.org/wiki/Light-emitting_diode
https://www.pantechsolutions.net/fiber-optics-laser-diode-module
Important Books/Journals for further learning including the page nos.:
Engineering Physics, Dr.G.SudarMozhi, Sri kandhan Publication,2016. Page No.4.22-4.26

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LECTURE HANDOUTS L 27

PHYSICS
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Course Name with Code : ENGINEERING PHYSICS /21BSS01

Course Faculty : Date of Lecture:

Unit : III - FIBER OPTICS AND ITS APPLICATIONS

Topic of Lecture: Detectors , Endoscope

Introduction :
The commonly used detectors are;
 p-i-n photo diode and
 Avalanche photodiode.
Endoscope
Fibre endoscope is used to study the interior parts of the human body that cannot be viewed directly.
Prerequisite knowledge for Complete understanding and learning of Topic:
 To know the basic knowledge about the Principle of photodiode.

Detailed content of the Lecture:

. Detectors perform the reverse function of fibre optic sources. They convert light energy into electrical
energy at the receiving end of the fibre optic communication. The commonly used detectors are;
1) p-i-n photo diode and
2) Avalanche photodiode.
p-i-n photodiode
p-i-n photodiode detector works on the principle of reverse bias. When a photon is made to
incident on the intrinsic region of the diode, the electrons in the valence band is move towards the
conduction band and thus creating electron-hole pair. These electrons and holes are accelerated by the
external electric field which results in photocurrent. Thus light is converted into electrical signal.
Construction
It consists of three regions viz, p, i and n. The p-region is highly doped with the
positive charge carriers and n-region is highly doped with negative charge carriers. The central i-
region is a neutral region lightly doped with n-material.
 p-i-n photodiode.
Working
The pin photodiode is applied with high reverse bias voltage. When a photon (of energy greater
than or equal to the band gap energy of the photodiode) is incident on the depletion region (i), the
electron-hole pair is created due to the absorption of photon. These charges are accelerated by the
applied voltage which gives rise to photo current. The photo current produced is directly proportional
to the incident light energy.
Avalanche photodiode
In this diode enormous electron-hole pairs are created from a single electron-hole pair by
collision process.
Principle
This diode works on the principle of reverse bias. When light is made to incident on the intrinsic
region, electron-hole pairs are generated. By avalanche effect more number of electron-hole pairs is
created which results large photocurrent is produced than p-i-n photodiode
Construction
It consist of four different regions viz, p+, i, p and n+. The layer-1 is made of heavily doped n-
region (n+).The layer-2 is made of p-region. The layer-3 is lightly doped with p material called
intrinsic region (i) and the layer-4 is heavily doped with p-material (p+).

Avalanche photodiode
Working
When the light is incident on the intrinsic region under reverse bias condition, the light is
absorbed and thus electron-hole pair creates. When the biasing voltage is increased, the generated
electron moves into p-region (layer-2) and n+ region (layer-1). These electrons collide with free
electrons in n+ region and release more number of free electrons and thus avalanche is produced. In
this way a single photo generated electron releases thousands of free electrons and produce enormous
output current. Since large current is produced with a single photon on the diode, the detectors are
termed as sensitive detector.
ENDOSCOPE
The fibre endoscope consists of bundle of flexible fibres containing up to 140000 thin optical
fibres of few mm thicknesses. Fibre endoscope is used to study the interior parts of the human body
that cannot be viewed directly.
The endoscope consists of two fibres called inner and outer fibers.

Fiber endoscope

Video Content / Details of website for further learning (if any):

https://en.wikipedia.org/wiki/Endoscope
https://www.cancer.net/navigating-cancer-care/diagnosing-cancer/tests-and-procedures/types-
endoscopy

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LECTURE HANDOUTS L 28

PHYSICS
I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : IV Crystal Physics Date of Lecture:

Topic of Lecture: Crystals, Lattice, Unit cell, Bravais lattice

Introduction :
Matter is divided into three states namely solids, liquids and gases.
solids are classified into two categories based on the arrangement of atoms or molecules.
The classifications of solids are, Crystalline solids and Non crystalline solids or amorphous
solids
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on atomic structure of the materials

Detailed content of the Lecture:

Crystals
 The materials possessing such a regular arrangement of atoms are called crystals.
 Each atom is at regular interval along with the other atoms in all direction
 Crystalline solids have directional properties, they are called as anisotropic substances.
 Example: Copper, Silver, Nickel, Iron, etc.
Non-crystalline solids or Amorphous Solids
 The solid substance in which the atoms or molecules are arranged randomly (not regular) is called non-
crystallize solid or Amorphous solid.
 These types of substances are called isotropic substances.
 Example: Glass, Plastic and Rubber.
Lattice:
 The crystals are having regular and periodic arrangement of atoms.
 A lattice or space lattice is defined as an array of points in three dimensions and
have identical surroundings to that of every other point.
Unit Cell:
 The unit cell is defined as the smallest geometrical unit which when repeated in space over three
dimensions gives the actual crystal structure
 A unit cell is the smallest volume that carries full description of the entire lattice.
BRAVAIS LATTICES
 There are fourteen different ways of arranging points in space lattice from the 7 crystal systems.

S. Name of the
Type of unit cell
No. System
i) Simple
1 Cubic ii) Body centered
iii) Face centered
i) Simple
2 Tetragonal ii) Body centered
i) Simple
ii) Body centered
3
Orthorhombic iii) Face centered
iv) Base centered
i) Simple
4 Monoclinic
ii) Base centered
5 Triclinic i) Simple triclinic
6 Trigonal i) Simple trigonal
7 Hexagonal i) Simple hexagonal
Video Content / Details of website for further learning (if any):
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https://www.youtube.com/watch?v=VPCDSmoomGk

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LECTURE HANDOUTS L 29

PHYSICS
I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : IV Crystal Physics Date of Lecture:

Topic of Lecture: Lattice planes and Miller indices

Introduction :

A lattice or space lattice is defined as an array of points in three dimensions and have identical
surroundings to that of every other point.
 Lattice points representing the locations of atoms in an imaginary geometry. The actual array of atoms
is called the structure.
 A Set of equally spaced planes containing lattice points are called lattice planes or atomic planes.
 A set of three numbers are introduced with in the parentheses by Miller and is called Miller indices.
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on atomic structure of the materials

Detailed content of the Lecture:

Miller indices.
Miller indices are defined as the reciprocal of the intercepts made by the plane on the crystallographic
axes in the smallest numbers.
 The integers should be enclosed with in the bracket i.e. (1 1 1 )
 Comma or dot between any two numbers in the bracket may be avoided
 The Miller indices for any plane say (1 3 2) should be read as one three two only
Salient features of Miller indices
 A plane parallel to any coordinate axis will meet at infinity only. The intercept of this plane is
considered as infinity. Hence the Miller indices for that particular axis are zero
 A plane passing through the origin has non zero intercept
 All equally spaced parallel planes have same Miller indices
Steps to find out

Miller indices
 Find the intercepts made by the plane (ABC) along the three axes and expressed in terms of axial
lengths. OA: OB : OC = 1a : 2b :2c

 Find the co-efficient of the intercepts i.e, 1, 2, 2

 Find the reciprocals of intercepts
 Convert these reciprocals into whole numbers by multiplying each reciprocal with the LCM. In this case
2 is the LCM. The numerator values are: 2 1 1
 Enclose all these numbers within the parenthesis (bracket) (2 1 1)
Some examples of Miller indices of cubic crystal planes

Video Content / Details of website for further learning (if any):

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https://www.youtube.com/watch?v=n84gzYlB0BQ

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LECTURE HANDOUTS L 30

PHYSICS
I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : IV Crystal Physics Date of Lecture:

Topic of Lecture: d - spacing in a cubic lattice

Introduction :
 d-spacing or the inter planar distance is the distance between any two successive lattice planes.
 Relation between the inter planar distance(d),lattice constant (a) and miller indices (hkl)
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on atomic structure of the materials

Detailed content of the Lecture:

d - spacing in a cubic lattice

 OX, OY and OZ represents the axes and OA, OB, OC are the intercepts by the plane.
 α, β and γ represents the angle between ON and along with other axis OA, OB and OC respectively.
a a a
 The intercepts of the plane on the three axes are OA  , OB  , OC 
h k l

a a a
  OA : OB : OC  : :
h k l

From  ONA, From  ONB,

ON d dh ON d dk
cos     cos    
OA a h a OB a k a
 From  ONC ,
dh dk dl
ON d dl  cos  : cos  : cos   : :
cos     a a a
OC a l a

2 2 2
 dh   dk   dl 
cos   cos   cos   1 ,          1
2 2 2

 a   a  a

d2 2
2 
or h  k2  l2   1
a
a2
d2  2
h  k2  l2

a
or d 
h2  k 2  l 2
 The above equation gives the relation between inter atomic distance ‘a’ and the inter planer
distance‘d’ and is called d-spacing.
 The interplanar distance between (100) plane is,
a
d100  a
1  02  02
2

 The interplanar distance between (110) plane is

a a
d110  
1 1  0
2 2 2
2

 The interplanar distance between (111) plane is

a a
d111  
1 1 1 2 2 2
3
1 1
 d100 : d110 : d111  1: :
2 3
Video Content / Details of website for further learning (if any):
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https://www.youtube.com/watch?v=7VutiZCgKAk

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LECTURE HANDOUTS L 31

PHYSICS
I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : IV Crystal Physics Date of Lecture:

Topic of Lecture: Calculation of number of atoms, atomic radius, Packing factors for simple cubic
structure (SC)
Introduction :

The total number of atoms present in a unit cell is called number of atoms per unit cell.

Atomic radius is defined as half of the distance between any two nearest neighbouring atoms in the
crystal structure.
 Co-ordination number is defined as the number of nearest neighbouring atoms to any particular atom
in the crystal structure.
 Packing factor is the ratio of the total volume occupied by the atoms in a unit cell (v) to the total
volume of a unit cell (V).
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on atomic structure of the materials.

Detailed content of the Lecture:

 Number of atoms per unit

1
cell 8  1
8
a
 The lattice constant, a = 2r, or Atomic radius r 
2
 The coordination number for simple cubic is 6.

Volume occupied by the total number

of atoms per unit cell
 Atomic Packing Factor =
Total volume of the unit cell
 Volume occupied by the total number  4 a 3
3
4 4 a
   1   r 3
,  1     
of atoms per unit cell (v)  3 3 2 24

Volume of the unit cell (V )  a  a  a  a 3

v  a3 6 
 APF   3
 or APF  0.52
V a 6
 Atomic Packing Factor for simple cubic structure = 0.52
 It is understood that only 52 % of volume of the unit cell is only occupied by the atoms and the
remaining area is kept vacant.

Video Content / Details of website for further learning (if any):

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https://www.youtube.com/watch?v=rroulXtAxXk

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LECTURE HANDOUTS L 32

PHYSICS
I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : IV Crystal Physics Date of Lecture:

Topic of Lecture: Calculation of numberf of atoms, atomic radius, Packing factors for
body centered cubic structure (BCC)
Introduction :

The total number of atoms present in a unit cell is called number of atoms per unit cell.

Atomic radius is defined as half of the distance between any two nearest neighbouring atoms in the
crystal structure.
 Co-ordination number is defined as the number of nearest neighbouring atoms to any particular atom in
the crystal structure.
 Packing factor is the ratio of the total volume occupied by the atoms in a unit cell (v) to the total volume
of a unit cell (V).
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on atomic structure of the materials.

Detailed content of the Lecture:

1
 Number of atoms due to corner atom per unit cell 8  1
8
 Number of atoms due to body centered atom / unit cell = 1
 Total number of atoms per unit cell in BCC = 1 + 1 = 2
 Atomic Radius- BCC structure
DF 2  FG 2  GD 2
 FG 2  GC 2  CD 2
  a2  a2  a2 From the diagram, DF  4r
 3a2 a 3
Hence 4r  a 3 , r 
or DF  a 3 4

a 3
Atomic radius of a BCC structure r 
4
 Coordination number of BCC structure is 8
v
 Atomic Packing Factor =
V
4
Volume of two spherical atoms  v   2  r
3

3 a 3
r
8 4
 r
3

3
8 a 3  8  a 3 3 
3
3
3
  ,   ,  a 8
3

3  4 
 3  64 
 Volume of the unit cell of a cubic system (V) = a3
v a 3 3 8  3
Atomic Packing Factor = ,  3
,  0.68
V a 8
 Atomic packing factor for BCC structure = 0.68
 It is understood that 68 % of volume of the unit cell is occupied by the atoms and
the remaining is kept vacant

Video Content / Details of website for further learning (if any):

https://www.youtube.com/watch?v=8gJDNvOYiEA
https://www.youtube.com/watch?v=SZLAwTCMYzY

Important Books/Journals for further learning including the page nos.:

Sudarmozhi.G., Engineering Physics I , Bharath Publishers , 2015,Page no.1.11-1.35

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LECTURE HANDOUTS L 33

PHYSICS
I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : IV Crystal Physics Date of Lecture:

Topic of Lecture: Calculation of number of atoms, atomic radius, Packing factors for
face centered cubic structure (FCC)
Introduction :
 The total number of atoms present in a unit cell is called number of atoms per unit cell.
 Atomic radius is defined as half of the distance between any two nearest neighbouring atoms in the
crystal structure.
 Co-ordination number is defined as the number of nearest neighboring atoms to any particular atom in
the crystal structure.
 Packing factor is the ratio of the total volume occupied by the atoms in a unit cell (v) to the total
volume of a unit cell (V).
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on atomic structure of the materials.

Detailed content of the Lecture:

 Total number of atoms per unit cell in FCC structure is 4

 Atomic radius of FCC structure

AC2 = AB2 + BC2

= a2 + a2
= 2a2
a 2
or AC = a 2 , From the diagram AC = 4r,Hence, 4r = a 2 , r =
4
 a 2
Atomic radius of FCC structure is =
4

 total number of nearest neighbours in FCC structure = 12

 Atomic packing factor

 Total number of atoms per unit cell of a FCC structure = 4

4
 Volume of 4 spherical atoms (v) = 4  r 3
3
16 3
= r
3
a 2
Since r  for FCC structure,
4

a 2  16  a 2 2 
3
16
3
a 3 2
v=   =   =
3  4  3  64  6

 Volume of the unit cell for a cubic structure (V) = a3

 Atomic packing factor =

a 3 2
6  2
3
=  0.74
a 6
 Atomic packing factor for FCC structure = 0.74
 In which 74% of volume of a unit cell is occupied by the atoms and remaining volume is vacant.
Video Content / Details of website for further learning (if any):
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https://www.youtube.com/watch?v=_h-Xv9nsJLc

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LECTURE HANDOUTS L 34

PHYSICS
I/I
Course Name with Code : Engineering Physics / 21BSS01
Course Faculty :
Unit : IV Crystal Physics Date of Lecture:

Topic of Lecture: Calculation of number of atoms, atomic radius, Packing factors for
Hexagonal closed packing structure (HCP)
Introduction :

The total number of atoms present in a unit cell is called number of atoms per unit cell.

Atomic radius is defined as half of the distance between any two nearest neighbouring atoms in the
crystal structure.
 Co-ordination number is defined as the number of nearest neighboring atoms to any particular atom
in the crystal structure.
 Packing factor is the ratio of the total volume occupied by the atoms in a unit cell (v) to the total
volume of a unit cell (V).
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on atomic structure of the materials.

Detailed content of the Lecture:

Hexagonal Close Packed Structure (Hcp)
 Total no. of atom per unit cell in HCP structure is 6

 Co-ordination number is 12
a
  Atomic radius r
2
 Atomic packing factor:

Volume of the atoms in a

4 3
unit cell, v = 6  r ,
3
Since atomic radius
a
r
2

24   a 
3

v   ,v
3 2
  a3
 Total volume of the HCP unit cell, V = Area of the base  height

 Area of the base = Area of 6 triangles

= 6  area of one triangle (OFA)
1
 area of the triangle OFA =  AF  OT
2
Substituting the value of OT from equation (1) and AF = a,
1 2 3 a2 3 a2 3 3 3 2
 Area of the triangle OFA = a = , Area of the base = 6  ,= a
2 2 4 4 2

3 3 2
 Total volume of the unit cell (V)  a c
2
 a3 2  a 
 Atomic packing factor = =  
3 3 2 3 3c
ac
2
2 3 
= = = 0.74
3 3 8 3 2
Atomic packing factor for HCP = 0.74

 74% of volume of the unit cell of HCP structure is occupied by the atoms and
remaining is kept vacant.

Video Content / Details of website for further learning (if any):

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LECTURE HANDOUTS L 35

PHYSICS
I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : IV Crystal Physics Date of Lecture:

Topic of Lecture: Crystal defects-point defect and line defect

Introduction :
 Crystal defect is generally used to describe the deviation from the perfect periodic array of atoms in
the crystalline materials.
 In an ideal crystal the atoms are arranged continuously in a perfect manner. But in real crystals,
irregularities, imperfections, defeats and lattice distortions are generally present.
 The electrical and magnetic properties of the crystalline materials are affected by the imperfections in
the crystals.
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on atomic structure of the materials.
 Basic knowledge on lattice, lattice plane, lattice vibration.
Detailed content of the Lecture:
 The crystalline defects are broadly classified based on their geometry.
 Point defects, Line defects, Surface defects and Volume defects.
Point defects
  Point defects are called zero dimensional defects.
 The defect due to imperfect packing of atoms during crystallization is called point defects.
 The point defect increases the internal energy of the crystal and hence the value of mechanical
strength at that point is reduced.
 Different types of point imperfections are Vacancies,Interstitials,Impurities,Electronic defeats

Line Defect

Line defects
 They are one dimensional imperfection and also called dislocations. A dislocation may be defined as a
disturbed region between two perfect parts of a crystal.
 The dislocation is responsible for the phenomenon of slip by which the metals are deformed plastically.
 It is connected with the mechanical phenomena such as creep, fatigue and brittle fracture and helpful in
explaining the crystal growth.
 The dislocations are arises due to i) Growth accidents ii) Thermal stresses iii) External stresses and iv)
Phase transformations.
 The voids and vacant sites in the crystals favours the generation of dislocations.
 The dislocations are of two types namely,Edge dislocation and Screw dislocation.
 Creation of extra half plane or a plane that does not extend up to the base of the crystal is called edge
dislocation.
 The displacement of the atoms in one part of the crystal related to the rest of the crystal is called screw
dislocation.
 The magnitude and direction of this dislocation can be determined with the help of Burger vectors.
Video Content / Details of website for further learning (if any):
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LECTURE HANDOUTS L 36

PHYSICS
I / II

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : IV Crystal Physics Date of Lecture:

Topic of Lecture: Crystal defects-surface defect, Burger vector

Introduction :
 They are two dimensional and also called plane defects. The surface defect is classified into
i) External Surface Imperfections and ii) Internal Surface imperfections.
 The external surface of a crystal is an imperfection in itself, as the atomic bonds do not extend beyond
the surface.
 Internal surface imperfection is due to change in stacking of atomic planes across the boundary
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on atomic structure of the materials.
 Basic knowledge on lattice, lattice plane, lattice vibration..
Detailed content of the Lecture:

External surface imperfections

  The atoms on the surface may be visualized and it cannot be compared with the atoms within the
crystal.
 The atoms on the surface have neighbours on only one side, where as the atoms inside the crystal have
neighbours on both side.
 The surface atom possesses energy higher than that of the internal atoms.

Internal surface imperfection

Grain Boundaries

 The grain boundaries are the surface imperfections which separate crystals of different orientations in a
poly crystalline aggregate.
Tilt or twist boundaries

 When the neighbouring crystalline regions tilted with respect to each other by a small angle are called tilt
or twist boundary.
Twin boundaries
 Surface imperfection which separate two orientations that are mirror images of one another are called
twin boundaries.
 Twin boundaries occur in pairs, that the orientation change introduced by one boundary is restored by the
other.
Stacking fault
 These imperfections caused due to fault in the stacking sequence of atomic planes. The FCC crystals
having stacking layers
Ferro magnetic domain walls
 When two ferromagnetic regions differ from one another due to the direction of magnetization, the
boundary between them is an imperfection and is called a ferromagnetic domain wall.
 The domain walls determine the magnetic properties of ferromagnetic materials.

Video Content / Details of website for further learning (if any):

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Important Books/Journals for further learning including the page nos.:

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LECTURE HANDOUTS L 37

PHYSICS
I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : V Properties of matter and thermal physics Date of Lecture:

Topic of Lecture: Elasticity, Hooke’s law, Relationship between three modulii of Elasticity
Introduction :
 Elasticity is the property by virtue of which material bodies regain their original shape and size after the
external deforming forces are removed.
 When the external force acts on a body, there is a change in its length, shape and volume. If a body
recovers its original shape, size or volume completely on the removal of external forces, it is called
perfectly elastic body.
 The bodies which do not regain their original shape and size are called plastic bodies.
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on elastic properties of the materials

Detailed content of the Lecture:

Stress
 The restoring force per unit area over the elastic material is called stress.
 Restoring force per unit area perpendicular to the surface is called normal stress and the restoring
force parallel to the surface per unit area is called tangential stress.
Strain
 Strain is defined as the ratio of the change in shape to the original shape. Strain being ratio has no
units. Longitudinal Strain, Shearing strain and Volume strain
HOOKE’S LAW
 The relationship between strain and stress is called Hooke’s Law. According to this law stress is directly
stress
proportional to strain within the elastic limit. = E
strain
 E is a constant called coefficient of elasticity or modulus of elasticity.
 Elastic Limit: The maximum stress up to which a body exhibits the property of elasticity is called
elastic limit.
Relationship between three modulus of Elasticity
  Young’s Modulus (Y), Bulk modulus (K), Rigidity modulus (  )

the relation between Y,  and as

Y
  and       (1)
2(1   )
The relation between Y, K and as
Y
K        (2)
3(1  2 )
Re arranging equation (1), we have
Y
2  2        (3)

Re arranging equation (2), we have
Y
1  2        (4)
3K
Adding equation (3) and (4), we have
Y Y
3 
3K 
 1 1
 Y  
 3K  
3   3K

Y 3K
1   3K
or 
Y 9 K
9 K
or Y  is Relationship between three modulus of Elasticity
  3K
Video Content / Details of website for further learning (if any):
https://www.youtube.com/watch?v=HALbtyDUjp0
https://www.youtube.com/watch?v=D5vnqohxEOI

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Sudarmozhi.G., Engineering Physics I , Bharath Publishers , 2015, Page no.2.1-2.7

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LECTURE HANDOUTS L 38

PHYSICS
I/I
Course Name with Code : Engineering Physics / 21BSS01
Course Faculty :
Unit : V Properties of matter and thermal physics Date of Lecture:

Topic of Lecture: Stress- strain diagram, Poisson’s ratio, Factors affecting elasticity
Introduction :

The elastic properties of the metals can be studied under uniform stress using stress-strain
diagram.
 Poisson’s ratio is the relation between lateral strain and longitudinal strain
 Various factors such as temperature, stress and impurity affect the elastic property of the
materials,depends on the factors elasticity may increase or decrease
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on elastic properties of the materials

Detailed content of the Lecture:

Stress- strain diagram

 The elastic properties of the metals can be studied under uniform stress using stress-strain diagram.
 When a material of uniform bar or wire is given stress continuously, the strain will be exhibit linearly
up to the point P and it obeys Hook’s law.
 Hook’s law holds good only for the straight line portion of the curve (OP) called elastic range.
 When the applied stress is withdrawn, the material regains its original condition between the points O
and P.
 The limit up to which the body regains its original condition when the stress is withdrawn is called
elastic limit.
 If the stress applied increases gradually beyond P, the strain increases more rapidly. When the stress is
removed in this range, the material does not regain its original condition. Hence this region is called as
plastic range.
 If the stress-strain relation is studied beyond the plastic range, it is observed that the wire loses its
 shape and become thinner in diameter and is breaks at the point R, called breaking point.
POISSON’S RATIO (γ)
 The ratio of lateral strain to longitudinal strain is called Poisson’s ratio.
Let the original length of the wire =L
Original Diameter of the wire =D
Increases in length =l
Decrease in diameter =d
Lateralstrain d D 
Poisson’s ratio,  = = 
Longitudinalstrain lL 
Where β is lateral strain and  is longitudinal strain.
Factors Affecting Elasticity
 Effect of temperature: a rise in temperature reduces the elastic property of a material.
 The material like carbon filament is highly elastic at room temperature.
 In certain cases like invar steel, elasticity is unaffected by the change in temperature.
 Effect of impurities: The addition of impurity atoms to any material reduces its elastic property.
 The impurity atoms generally having different atomic radii and hence it acts as the centre of distortion
and decreases the elastic property.
 Effect of hammering and rolling: While hammering or rolling, crystal grains break into smaller sizes
which results the increase of elastic property.
 Effect of annealing:When the material is heated and then cooled (annealing), large crystal grains are
formed in the crystalline structure. The larger crystal structure results in the reduction of the elastic
property.
 Effect of stress:When the material is stressed, the elastic property decreases gradually

Video Content / Details of website for further learning (if any):

https://www.youtube.com/watch?v=foE4IMFPAUE

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LECTURE HANDOUTS L 39

PHYSICS
I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : V Properties of matter and thermal physics Date of Lecture:

Topic of Lecture: Bending moment, depression of a Cantilever

Introduction :
 A beam is defined as the rod of uniform cross-section (circular or rectangular) whose length is large in
comparison to its breadth and thickness.
 Beams are used in the construction of bridges or for the purpose of supporting loads.
 A cantilever is a thin uniform beam fixed horizontally at one end and loaded with a weight at the other
end.

Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on elastic properties of the materials
 Knowledge on bending of beam and cantilever
Detailed content of the Lecture:
Bending moment of a beam

 Let a beam fixed at one end is loaded at the other end as shown in the Figure.
 The load acts vertically downwards at its free end and the reaction at the support acts vertically
upwards which constitute the external bending couple.
 Due to elasticity, a restoring couple is developed inside the beam. The moment of this elastic couple is
called the internal bending moment.
 When the beam is in equilibrium, External bending moment = Internal bending moment
Expression for the bending moment
 XY = Rθ and X'Y' = (R+ x)θ
 Increase in length = X'Y' – XY = (R+ x) θ – Rθ = x θ
increase in length x x
Linear strain =  
original length R R
Stress x
 Young's modulus Y = or Stress = Y×strain = Y
Strain R
 Force acting on the element of area of cross-section δA is F = Stress × Area
x
 Y A
R
 The forces producing elongation on the upper region and producing contraction on the lower
region of AB constitute a couple. Moment of the force about the neutral axis AB
 Yx 
   A x
R 
Yx  A
2

R
 The sum of moments of forces acting on all the filaments
Yx 2
  R A
Y

R
 x 2 A

Here x  A 
2
Ak 2  I g
 Where A is the area of cross-section and k is the radius of gyration. Ig is called the geometrical moment of
YI g
inertia of the beam. Hence bending moment 
R
Depression of a cantilever
 Let AB represents the neutral axis of a cantilever of length l, fixed at the end A and loaded at B with a
weight W. The end B is depressed to the position B'. The neutral axis AB shifts to the position AB'
 Consider an element PQ at a distance x from the fixed end A. the moment of the external couple or the
deflecting couple = W (l - x)
YI g
 The moment of restoring couple or bending moment =
R
 YI g
 Under equilibrium conditions both the moments are equal. W (l  x)        (1)
R
 Where R is the radius of curvature of the neutral axis at P. let us consider the point Q at a smaller
distance dx from P.
Let  POQ  d
or PQ  R d  dx
dx
 R       (2)
d
Substituting equation (2) in equation (1), we get
 d 
W (l  x)  YI g  
 dx 
W (l  x) dx
or d       (3)
YI g

 Draw tangents at P and Q and they meet at C and D. The angle between the tangents at P and Q
is also equal to dθ. The depression CD = dy, Then dy = (l - x) dθ ----- (4)
W (l  x) dx
2
Substituting the value of dθ from equation (3) dy 
YI g
Total depression caused by the load is

W (l  x) 2
l
y  
0
YI g
dx

l
W
 l  2lx  x 2 ) dx
2

YI g 0

l
W  2 2lx 2 x3 
 l x   
YI g  2 3 0
Wl 3
y        (5)
3YI g

Video Content / Details of website for further learning (if any):

https://www.youtube.com/watch?v=7IeJgDSQkaw
https://www.youtube.com/watch?v=C-FEVzI8oe8

Important Books/Journals for further learning including the page nos.:

Sudarmozhi.G., Engineering Physics I , Bharath Publishers , 2015, Page no.2.8-2.14

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LECTURE HANDOUTS L 40

PHYSICS
I/I
Course Name with Code : Engineering Physics / 21BSS01
Course Faculty :
Unit : V Properties of matter and thermal physics Date of Lecture:

Topic of Lecture: Young’s modulus by uniform bending, I-shaped girders

Introduction :
 The ratio of the longitudinal stress to the longitudinal strain within the elastic limit is called Young’s modulus of
elasticity. The unit of Young’s modulus is N/m2.
 If load is applied on both end of the beam and elevation is take place at the centre portion is called as uniform
bending.
 The girders in the form of I-shape are called as I-shape grider.They are used in building construction.
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on elastic properties of the materials
 Knowledge on uniform bending and non uniform bending
Detailed content of the Lecture:
Young’s modulus by uniform bending

 Let AB is a beam supported on two knife edges C and D. Let CD = l. Equal weights are suspended at its ends A
and B.Let AC = BD = a.
 The reactions at each knife edge act upwards.
The beam bends into an arc of a circle of radius R. The elevation of the midpoint of the beam is y.
 The external bending moment with respect to P
= W (AP) – W (CP) = W (AP– CP) = W (AC) = Wa
 YI g
 This external bending moment must be balanced by the internal bending moment
R
YI g
  Wa
R

1 Wa
       (1)
R YI g

EF (2R - EF) = CF2 = y (2R - y) = (l/2)2

l2
y 2R  ( y 2 neglected )
4
l2
y        (2)
8R

Wal 2
Substituting (1) in (2) y 
8YI g

bd 3
Substituting I g  for a rectangular beam and W = mg,
12
mgal 2
y 
8Y (bd 3 12)
3mgal 2
or y 
2bd 3Y
I-shaped girders

 When a beam is depressed by applying a load, the layers above the neutral axis are elongated whereas the
layers below the neutral axis are compressed.
 In which the central layer called neutral axis remains unaltered.
 The compression or elongation is proportional to the distance from the neutral surface.
 It is observed that the stress produced in the beams is maximum at the upper and the lower surfaces of the
beam.
 Maximum amount of material will have to be located at these portions of maximum stress.
 The portions in between the top and bottom of the girder may have little stress or nil stress and
hence they will be removed.
 A girder in the form of a rectangle or I- shaped will have the same strength.
 This is the reason for using the iron girders in the form of I shaped.
 This provides a high bending moment and thus large amount of material can be saved.
Video Content / Details of website for further learning (if any):
https://www.youtube.com/watch?v=VoMrynNIceM

Important Books/Journals for further learning including the page nos.:

Sudarmozhi.G., Engineering Physics I , Bharath Publishers , 2015, Page no.2.15-2.18

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LECTURE HANDOUTS L 41

PHYSICS
I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : V Properties of matter and thermal physics Date of Lecture:

Topic of Lecture: Modes of heat transfer

Introduction :
 When the temperature of a body increases, energy is said to be supplied to a body and is stored in the
form of heat energy.
 Heat energy may be given to a body either by conversion of energy from some other form or by
transferring heat from some other place.
 The heat energy is transmitted from the region of higher temperature to the region of lower
temperature by the processes namely, Conduction, Convection and Radiation

Prerequisite knowledge for Complete understanding and learning of Topic:

 Basic knowledge on Heat and thermodynamics

Detailed content of the Lecture:

Conduction
 When two bodies, one at higher temperature and another at lower temperature are kept in contact
with one another, the temperature of the hot body decreases gradually, whereas the temperature of
the cold body increases i.e., the heat energy is transferred from a body at higher temperature to a body
at lower temperature.
 When the heat is supplied at one end of a metallic rod ,it is observed that the temperature of the other
end increases gradually. This shows that the heat energy is transferred from the hotter end to the colder
end. This kind of transfer of heat energy is called thermal conduction.
 Conduction is possible only in solid materials. Conduction cannot take place in liquids, gases and in
vacuum.
 When the temperature at the one end is increases, the molecules start vibrating, collide with the
neighbouring molecules and transfer some of their vibrating energy.
  The neighbouring molecules now start vibrating and transfer the energy again. Thus the heat transfers
from one end to the other end by vibration without the actual movement of molecules. i.e., the
particles remain in their mean positions of equilibrium.
 Conduction is the mode of transfer of heat from a hotter part of the body to its colder part, without
the actual movement of the particles.
Convection
 Convection is the process in which heat transfer takes place by the actual movement of heated
particles. This is possible only in liquids and gases.
 A beaker containing water or any other liquid is heated by means of a burner. The heat energy is initially
supplied to the lower region of the beaker.
 The water in this lower region becomes warmer and its density is decreased. The density of the water in
the upper region is comparatively high than the water in the lower region.
 The water with less density in the lower region starts moving upwards replacing by the colder water
particles.
 The cold water reaches the lower portion becoming warmer, move upward and again replaced by the
cold water.
 It is concluded that the heat is transferred from one region to another region by the actual movement
of heated particles of the medium. Such a process is called convection.
 Convection is the mode of transfer of heat from one part of the medium to another part by the actual
movement of the heated particles.
Radiation
 The process of conduction and convection requires the presence of material medium between the
source and the receiver for the energy transfer.
 However, material medium is not necessary for radiation.
 It can travel through vacuum too. The heat radiations are electromagnetic in nature like light waves.
 The heat reaches from an electric lamp or from the sun is an example for the radiation.
 The radiation is the mode of transfer of heat from one body to another body without heating the
intervening medium.

Video Content / Details of website for further learning (if any):

https://www.youtube.com/watch?v=FTSBtx5jhaY
https://www.youtube.com/watch?v=MUC098hvqH4
Important Books/Journals for further learning including the page nos.:
Sudarmozhi.G., Engineering Physics I , Bharath Publishers , 2015, Page no.2.18-2.21

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LECTURE HANDOUTS L 42

PHYSICS
I/I
Course Name with Code : Engineering Physics / 21BSS01
Course Faculty :
Unit : V Properties of matter and thermal physics Date of Lecture:

Topic of Lecture: Thermal conductivity, Newton’s law of cooling

Introduction :
 The co-efficient of thermal conductivity is defined as the quantity of heat flowing is one second
through a unit cube of material when its opposite faces are maintained at a temperature difference of
1ºC.
 The unit of thermal conductivity is W/m/k.
 Newton’s law of cooling, for a small temperature difference between the body and its surrounding, the
rate of cooling of a body is directly proportional to the temperature difference and the surface area.
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on Heat and thermodynamics

Detailed content of the Lecture:

Thermal conductivity

 A solid material slab having thickness x and area of cross-section A.

 The opposite faces of the cube are maintained at the temperatures θ1 and θ2, where θ1 > θ2.
 The heat will start flowing from hot face to cold face and the direction of flow of heat will be normal to
the two faces of the slab.
 The quantity of heat conducted (Q) from one face to another depends upon the following factors.
 Q ∞ Area of cross-section (A)
∞ Temperature difference between the two faces (θ1- θ2)
∞ Time of conduction (t)
∞ 1/x (inversely proportional to the thickness of the slab x)
In general, the heat conduction
A(1   2 ) t
Q 
x
KA(1   2 ) t
Q 
x
Qx
K 
A(1   2 )t
Where, K is a constant called the coefficient of thermal conductivity of the material of the slab.
If A =1, (θ1- θ2) = 1, t =1 and x = 1,
K=Q
Newton’s law of cooling
 According to Newton’s law of cooling, for a small temperature difference between the body and its
surrounding, the rate of cooling of a body is directly proportional to the temperature difference and
the surface area.
dT
  k (T  T0 )
dt
 When dT dt the rate of cooling, k the constant is depends on the nature of the surface involved and

the surrounding temperature, T the temperature of the body and T0 is the temperature of the
surrounding.
 The –ve sign indicates that T >To and dT dt is the negative quantity i.e., temperature decreases with

time.

Video Content / Details of website for further learning (if any):

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https://www.youtube.com/watch?v=brU-cAK0-8Q&vl=en

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Sudarmozhi.G., Engineering Physics I , Bharath Publishers , 2015, Page no.2.21-2.25

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LECTURE HANDOUTS L 43

PHYSICS
I/I
Course Name with Code : Engineering Physics / 21BSS01
Course Faculty :
Unit : V Properties of matter and thermal physics Date of Lecture:

Topic of Lecture: Linear heat flow Lee’s disc method

Introduction :

Linear heat flow: Flow of heat along the linear path of the material

This method is used to determine the thermal conductivity of poor conductors like glass, wood, cork
etc.
Prerequisite knowledge for Complete understanding and learning of Topic:
 Basic knowledge on Heat and thermodynamics

Detailed content of the Lecture:

Lee’s Disc Method

 This method is used to determine the thermal conductivity of p oor conductors like glass, wood, cork
etc.
 The apparatus consists of a cylindrical steam chamber A through which steam can be passed. This
chamber A is placed over a metallic disc D.
 The given bad conductor (C) having same area of cross – section as that of the disc D, whose thermal
conductivity is to be determined is placed between them (A and D).
  Two thermometers T1 and T2 are inserted, one in the chamber A and other in the metallic disc D. θ1
and θ2 are the temperatures recorded by the thermometers T1 and T2 respectively.
 Steam is passed through the chamber and the temperatures recorded by the thermometers T1 and T2
are noted after the steady is reached. The heat passing through C in one second is equal to the heat
radiated by the exposed surface of C in one second.
KA(1   2 ) d  A  S 
  ms
x dt  2 A  S 

 A S 
 Where,  is the total area exposed to the surrounding. A is the area of cross section of D or
 2 A  S 
C, S is the area of the curved surface of D.
d
 is the rate of cooling at temperature θ2, m is the mass and S is the specific heat of the material
dt
D.
 The disc C is then removed and makes the disc D in direct contact with the steam chamber A. when
the temperature of D reaches about 10ºC higher than θ2, the disc D is gently removed and placed
over two knife edges.
 The fall of temperature is noted at a frequent interval of time.
 A graph is drawn between temperature and time.
d
 The value of at a temperature θ2 is found. By knowing all the values, the thermal conductivity K
dt
can be calculated.

Video Content / Details of website for further learning (if any):

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Important Books/Journals for further learning including the page nos.:

Sudarmozhi.G., Engineering Physics I , Bharath Publishers , 2015, Page no.2.26-2.27

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LECTURE HANDOUTS L 44

PHYSICS
I/I

Course Name with Code : Engineering Physics / 21BSS01

Course Faculty :
Unit : V Properties of matter and thermal physics Date of Lecture :

Topic of Lecture: Radial heat flow, Rubber tube method,

Introduction :
 Radial flow of heat: Flow of heat along the radial distance of the cylindrical tube.

Prerequisite knowledge for Complete understanding and learning of Topic:

 Basic knowledge on Heat and thermodynamics

Detailed content of the Lecture:

Radial heat flow

 Thermal conductivity can be determined by radial heat flow method and the quantity of heat flowing
per second is determined by using a constant flow calorimeter.
 Calorimeter with stirrer is used for the determination of thermal conductivity of rubber.
 The calorimeter is kept inside the wooden box and the space between them is filled with some
insulating material to avoid heat loss.
 Initially an empty calorimeter is weighed (m 1) and then filled with water. The mass of the calorimeter
with water is weighed again. The mass of the water is m2.
 Let ‘l’ be length of the rubber tube immersed in water. Using thermometer the initial temperature of
water is noted as θ1, Steam is passed through one end of the tube.
 The contents of the calorimeter are stirred well. The heat will flow radially through the wall of the
 rubber tube to the outer surface.
 Temperature of water out side the rubber tube is raised. Steam is cut off for a known period of time‘t’.
Now the water is stirred well and the temperature is noted again as θ2.
 The average temperature of the outer surface is (1   2 ) / 2 . Let r1 and r2 be the inner and outer radii

of the tube.
 The quantity of heat flowing through the tube per second
(m1s1 +m 2s 2 )(θ 2 -θ1 )
Q= --------- (1)
t
 Where, s1 and s2 are the specific heats of calorimeter and water. The thermal conductivity of rubber
can be determined using the radial heat flow equation,
Q log( r2 r1 )
K= ------------ (2)
2 lt
Substituting the value of Q from equation (1) in equation (2)
(m1s1 +m 2s 2 )(θ 2 -θ1 )log( r2 r1 )
K=
2 lt

Video Content / Details of website for further learning (if any):

https://www.youtube.com/watch?v=PkcGgaxujJg
https://www.youtube.com/watch?v=X4OzT-wYC_8

Important Books/Journals for further learning including the page nos.:

Sudarmozhi.G., Engineering Physics I , Bharath Publishers , 2015, Page no.2.22-2.23

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LECTURE HANDOUTS L 45

PHYSICS
I/I
Course Name with Code : Engineering Physics / 21BSS01
Course Faculty :
Unit : V Properties of matter and thermal physics Date of Lecture:

Topic of Lecture: Conduction through compound media (series and parallel)

Introduction :
 Conduction of heat through compound media is the flow heat through more than one
media, it may be joined together in series or parallel mode.

Prerequisite knowledge for Complete understanding and learning of Topic:

 Basic knowledge on Heat and thermodynamics

Detailed content of the Lecture:

Conduction through compound media (bodies in series)

 Consider a slab made of two different materials A and B of thickness x1 and x2.
 Let θ1 and θ2 are the temperatures of the end faces of the slab and θ is the temperature of the
common surface.
 K1 and K2 are the thermal conductivity of the materials A and B respectively.
 The heat is assumed to flow from A to B i.e., θ1 > θ2.
 When the steady state is reached, the same amount of heat will flow across any cross-section of a slab.
 K 1 A(1   )
 For the material A,The amount of heat flowing, Q 
x1

 For the material B,

K 2 A(   2 )
The amount of heat flowing, Q 
x2
In the steady state condition,
K 1 A(1   ) K 2 A(   2 )
Q  
x1 x2
K1 A1 K1 A K A K 2 A 2
  2 
x1 x1 x2 x2

K1 A1 K 2 A 2 K 2 A K1 A
  
x1 x2 x2 x1

K1 A1 K 2 A2 K K 
or    2  1 
x1 x2  x2 x1 
K11 K1
or  x1
 x 
1

  K 1 1 x1
K 1 x1
By substituting the values, the heat flowing through a compound section can be calculated.

Conduction through compound media (bodies in parallel)

 Consider a slab made of two different materials arranged in parallel as shown in Figure.
 Let K1 and K2 are the thermal conductivities of two materials of thickness x1 and x2 respectively.
  θ1 and θ2 are the temperatures of two opposite faces. A1 and A2 are the area of cross-section of the
materials.
 The amount of heat flowing (Q1) across the material of cross-section A1 is
K1 A1 (1   2 )t
x1

 The amount of heat flowing (Q2) across the material of cross-section A2 is

K 2 A2 (1   2 )t
x2
 The total heat flowing will be the sum of these two heats.
 Total heat flowing in t seconds through the compound media Q,
K1 A1 (1   2 )t K 2 A2 (1   2 )t
 
x1 x2

K A K A 
 (1   2 )t  1 1  2 2 
 x1 x2 

K i Ai
 (1   2 )t 
xi

Q KA
rate of heat flow   (1   2 ) i i
t xi

Video Content / Details of website for further learning (if any):

https://www.youtube.com/watch?v=R-5McNR2274

Important Books/Journals for further learning including the page nos.:

Sudarmozhi.G., Engineering Physics I , Bharath Publishers , 2015, Page no.2.22-2.25

Course Faculty

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