R23

Engineering Physics
Laboratory Manual
 JNTUK-KAKINADA
Engineering Physics Laboratory
R23 -Regulation
(Common to ALL Branches)
(Any 10 of the following listed experiments)

1. Determination of radius of curvature of a given Plano-convex lens by Newton’s rings.

2. Determination of wavelengths of different spectral lines in mercury spectrum using diffraction grating
in normal incidence configuration.
3. Verification of Brewster’s law
4. Determination of dielectric constant using charging and discharging method.
5. Study the variation of B versus H by magnetizing the magnetic material (B-H curve).
6. Determination of wavelength of Laser light using diffraction grating.
7. Estimation of Planck’s constant using photoelectric effect.
8. Determination of the resistivity of semiconductors by four probe methods.
9. Determination of energy gap of a semiconductor using p-n junction diode.
10. Magnetic field along the axis of a current carrying circular coil by Stewart Gee’s Method.
11. Determination of Hall voltage and Hall coefficient of a given semiconductor using Hall effect.
12. Determination of temperature coefficients of a thermistor.
13. Determination of acceleration due to gravity and radius of Gyration by using a compound pendulum.
14. Determination of magnetic susceptibility by Kundt’s tube method.
15. Determination of rigidity modulus of the material of the given wire using Torsional pendulum.
16. Sonometer: Verification of laws of stretched string.
17. Determination of young’s modulus for the given material of wooden scale by non- uniform bending
(or double cantilever) method.
18. Determination of Frequency of electrically maintained tuning fork by Melde’s experiment.
Note: Any TEN of the listed experiments are to be conducted. Out of which any TWOexperiments may
be conducted in virtual mode.
References:
A Textbook of Practical Physics - S. Balasubramanian, M.N. Srinivasan, S. Chand Publishers, 2017.

Web Resources
• www.vlab.co.in
• https://phet.colorado.edu/en/simulations/filter?subjects=physics&type=html,prototype

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 List of Experiments

1. Determination of radius of curvature of a given Plano-convex lens by Newton’s rings.

2. Determination of wavelengths of different spectral lines in mercury spectrum using diffraction

grating in normal incidence configuration.

3. Determination of wavelength of Laser light using diffraction grating.

4. Estimation of Planck’s constant using photoelectric effect.

5. Determination of energy gap of a semiconductor using p-n junction diode.

6. Determination of temperature coefficients of a thermistor.

7. Determination of acceleration due to gravity and radius of Gyration by using a compound

pendulum.

8. Determination of rigidity modulus of the material of the given wire using Torsional pendulum.

9. Verification of Brewster’s law. (Virtual Lab)

10. Magnetic field along the axis of a current carrying circular coil by Stewart Gee’s Method.

(Virtual Lab)

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Course Objectives:

The learning objectives of this course are:

➢ To gain practical knowledge by applying methods to correlate with the theory

➢ Apply the analytical techniques and graphical analysis to the experimental data.

➢ To develop experimental skills of the students

Course Outcomes:

By the end of the course, the student will be able to

CO1 Apply principles of physics to perform a wide spectrum of experiments individually.

CO2 Interpret and analyze experimental data in various suitable formats, such as tables and

graphs.

CO3 Summarize a clear understanding of various experimental principles, instrumentation,

setups, and procedures.

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GENERAL INSTRUCTIONS:

➢ The objective of the laboratory is learning. The experiments are designed to illustrate phenomena in

different areas of Physics and to expose you to measuring instruments.

➢ Conduct the experiments with interest and an attitude of learning.

➢ You need to come well prepared for the experiment

➢ Work quietly and carefully (the whole purpose of experimentation is to make reliable measurements!)

and equally share the work with your partners.

➢ Be honest in recording and representing your data. Never make up readings or doctor them to get a

better fit for a graph. If a particular reading appears wrong repeat the measurement carefully. In any

event all the data recorded in the tables have to be faithfully displayed on the graph.

➢ All presentations of data, tables and graphs calculations should be neatly and carefully done.

➢ Bring necessary graph papers for each of experiment. Learn to optimize on usage of graph papers.

➢ Graphs should be neatly drawn with pencil. Always label graphs and the axes and display units.

➢ If you finish early, spend the remaining time to complete the calculations and drawing graphs. Come

equipped with calculator, scales, pencils etc.

➢ Do not fiddle idly with apparatus. Handle instruments with care. Report any breakage to the Instructor.

Return all the equipment you have signed out for the purpose of your experiment.

5
 NEWTON’S RINGS Experiment No:
Date:

Aim

To determine the radius of curvature of a given Plano- convex lens by forming Newton’s rings

Apparatus

Travelling microscope, Sodium vapour lamp, Plano-convex lens, Thick glass plate-2, Reading lens and Black
paper.

Theory

The radius ‘rn’ of the nth dark ring is given by the formula
rn2 = n R  ----------- (1)
When the film is enclosed between the Plano convex lens and glass plate in air and when light is incident normally
on the lens. R is radius of curvature of the lens and λ is the wavelength of the light used. The radius ‘rm’ of ‘m’th
ring is given by
rm2 = m R  ----------- (2)
Suppose Dm and Dn are the diameters of the mth and nth dark rings.
Dm2 = 4 mR Dn2 = 4 nR
Dm2 − Dn2 = 4 (m − n) R
Dm2 − Dn2
R= ------------ (3)
4 ( m − n )
The radius of curvature the convex lens (R) can be determined using the Expression (3).

Procedure

The arrangement consists of a sodium lamp ‘S’, Plano convex lens of radius of curvature R, glass plate ‘P1’ and
glass plate ‘P2’ which is inclined at an angle of 45o with the horizontal as shown in Figure (1).

6
The light rays from the source ‘S’ incident normally on the lens system because of the glass plate ‘P2’. As a result
of interference between the light reflected from the lower surface of the lens and top surface of the glass plate ‘P1’,
concentric rings known as Newton’s rings, with alternate bright and dark rings having a central black spot seen
through the microscope as shown in figure (2). The microscope is properly focused, so that the rings are in a sharp
focus. In case if the rings are not uniformly bright, the glass plate is to be slightly adjusted. The rings so formed are
not to be disturbed till the experiment is completed.

The cross wires of the microscope set tangential to any one ring starting from the center of the ring system. The
microscope is moved to one side say left across the field of view. After passing beyond 20th ring, the direction of
motion of the microscope is reversed and the cross wire is set at 10th dark ring and the reading on the microscope
is noted. Similarly, the readings of the microscope for 8th, 6th and so on 2nd dark ring are noted. Now the
microscope is moved in the same direction and the readings corresponding to 2nd, 4th, 6th and so on 10th dark ring
on the right side are noted. The observations are recorded in the table.

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Graph

A graph is drawn with the ring number as abscissa (x-axis) and the square of the diameter as ordinate (y-axis) and
it will be a straight line. On the graph two numbers ‘m’ and ‘n’ are chosen and the corresponding values D2m and
D2n are used in equation (3) for the calculation of R. To determine the radius of curvature R of the lens, the
wavelength ‘λ’ of the source used is to be taken as 5893 x 10-8 cm from standard tables.

Least Count of Travelling Microscope

On main Scale 2 Divisions = 1 mm

1 Main Scale Division S = ½ mm
No. of vernier divisions N = 50
1 𝑚𝑎𝑖𝑛 𝑠𝑐𝑎𝑙𝑒 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛 1/2
Least Count = = = 0.01 mm or 0.001 cm
𝑁𝑜.𝑜𝑓 𝑣𝑒𝑟𝑛𝑖𝑒𝑟 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛𝑠 50

8
 Observations

Microscope readings (T.R = M.S.R + (V.C x L.C)) in cm

Order D2
Diameter
of the
S.No Left Right D=L~R
ring
in cm Cm2
M.S.R V.C V.C x L.C T.R (L) M.S.R V.C V.C x L.C T.R (R)

1
2

3
4

5
6

Precautions
1. The lens and the glass plate should be thoroughly cleaned with benzene or spirit.
2. Light should be incident normally on the lens
3. The radius of curvature of the lens should be large so that the diameter of the rings is large and the error in
finding the value of (Dm2 – Dn2) is small.
4. The central spot should be dark.

Calculations

Result
The radius of curvature of a given plano- convex lens is R = cm.

Signature of the Faculty

9
 Experiment No:
ENERGY BAND GAP OF A SEMICONDUCTOR Date:

Aim

To determine the energy band gap of a given semiconductor using a p-n junction diode.

Apparatus

A p-n junction diode, Thermometer, Copper vessel, Regulated DC power supply, Micro ammeter, Heater
& Bakelite lid.

Circuit

Formula
2𝑋2.303 𝑋𝑚𝑋𝐾𝐵
Eg= eV
1.6𝑋10−19

Where ‘Eg’ energy band gap of the given semiconductor diode, ‘m’ is slope of the straight line

KB is Boltzmann’s Constant = 1.38X10-23 J/K,‘Is’ reverse saturation current (µA),

‘T’ temperature (K)

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Procedure

Connect the two terminals of the given semiconductor diode to D.C power supply and micro ammeter in
such a way that the diode is reverse biased. Immerse diode in the oil bath. Insert the thermometer in the
oil the bath at the same level as that of the diode as shown in figure 1. Switch on the D. C. Power supply
and electrical heater, then the temperature of the oil bath gradually increases. Consequently, the current
through the diode also increase. When the temperature of the oil bath reaches to about 80 oC, then switch
off the heater. Stir the oil by means of a stirrer. Then, the temperature of the oil bath will rise and stabilizes
at about 95 oC. Note down the temperature of the oil bath and the current through the diode while cooling.
After few minutes, the temperature of the oil bath will begin to fall and the current through the diode
decreases. Note the value of the current for every 5 o C decrease of the temperature, till the temperature
of the oil bath fall to the room temperature.

Graph

Draw a graph with 1/T on x-axis and log10 Is on y-axis. The graph will be a straight line as shown in the
fig. From the graph find the slope of the straight line. The energy band gap of the given semiconductor
can be calculated by substituting the value of the slope in Formula of Eg

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Observations

S.No Temperature Temperature Reverse 1/T Log10 Is

Saturation
(oC) T (K) Current K-1

Is (µA)

Precautions

1. The diode and the thermometer should be immersed at the same level in the oil bath.

2. The temperature and the current should be noted simultaneously.

3. When the experiment is performed with Germanium diode, then the temperature should not exceed
80 oC

4. The experiment should be performed by connecting the diode in the reverse biased position.

Calculations

Result

The energy band gap of the given semiconductor material is E g = eV

Signature of the Faculty

12
 DIFFRACTION GRATING - NORMAL INCIDENCE METHOD Experiment No:
Date:

Aim

To determine the wave lengths of a given light using diffraction grating in normal incidence method.

Apparatus

Plane diffraction grating, Spectrometer, Mercury light, Reading lens.

Description

A plane diffraction grating consists of a parallel sided glass plate with equidistant parallel lines drawn
very closely on it by means of a diamond point. 15,000 lines per inch or (15,000 / 2.54) lines per cm are
drawn on the grating. Such gratings are known as the original gratings. But, the gratings used in the
laboratory are exact replicas of the original gratings on a celluloid film. The celluloid film is fixed over
an optically plane glass plate. Care should be taken while handling the grating. It should be handled by
the edges of the plate.

Theory

A parallel beam of non-monochromatic light from the collimator of a spectrometer is made to fall normally
on a plane diffraction grating erected vertically on the prism table. The telescope initially in line with the
collimator is slowly turned to one side. A line spectrum will be noticed, and on further turning the
telescope the line spectrum will again be notices. While the former is called the first order spectrum, the
later is called the second order spectrum. On further rotating the telescope, the third order spectrum may
also be noticed, depending on the quality of the grating. But the number of order of spectra that can be
observed with a given grating is limited. With the light normally incident on a grating having N lines per
cm, if  is the angle of diffraction of a radiation of wavelength  in the nth order spectrum, then

n  N = sin 

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 sin 
or  =
nN

 sin  X 2.54 
or  =   cm
 n X 15,000 
Knowing  and n, the wavelength of light radiation is calculated by using above equation for the
normal incidence method.

Procedure

Preliminary adjustments of the spectrometer are made, focusing and adjusting the eye piece of the
telescope to a distant object. The grating table is to be leveled with a spirit level. The grating is mounted
on the grating table for the normal incidence. The slit of the collimator is illuminated with mercury light.
The direct reading is taken, the telescope turned from this position through 90 o and fixed in this position,
as shown in figure1. The grating is mounted vertically on the grating platform, the rulings on it being
parallel to the slit in the collimator. The platform is now rotated until the image of the slit as reflected by
the glass surface is seen in the telescope. The vertical cross wire is made to coincide with the fixed edge
of the image. The platform is fixed in this position. The vernier table is now rotated in the appropriate
direction through 45o, so that the rays of light from the collimator fall normally, on the grating.
The telescope is now released and rotated it so as to catch the first order diffracted spectrum one side, say
right (or left) as shown in figure-2. The point of intersection of the cross wires is set on each color and the
reading in vernier I and vernier II is noted. . The telescope is now focused to the direct ray passing through
the grating and the point of intersection of the crosswire is set on the direct ray. The reading in the vernier
I and vernier II is noted. The difference in the readings corresponding to any one gives the angle of

14
diffraction  for that line in the first order spectrum. Knowing, n and N, the wavelength () of the given
 sin  X 2.54 
source of radiation for different color lines are calculated using equation  =  cm .
 n X 15,000 

The number of lines per inch as marked on the grating is noted and the number of lines per cm is given
by:
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑙𝑖𝑛𝑒𝑠 𝑝𝑒𝑟 𝑖𝑛𝑐ℎ
N=
2.54

Least Count of Spectrometer

On main Scale 2 divisions = 1o = 60 ′
1 Main Scale Division S = 30 ′
No. of vernier divisions N = 30
1 𝑚𝑎𝑖𝑛 𝑠𝑐𝑎𝑙𝑒 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛 30′
Least Count = = = 1′
𝑁𝑜.𝑜𝑓 𝑣𝑒𝑟𝑛𝑖𝑒𝑟 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛𝑠 30

15
Observations

Number of lines per inch = 15000

Number of lines per cm N = 15000/2.54
Least count = 1 '
Direct reading VA = VB =

𝐒𝐢𝐧 
Spectral Telescope Readings Difference Sin  = cm
𝒏𝑵
Line Right sideVA’ Left sideVB’  1=VA’~ VA  2=VB’~ VB =( 1+ 2)/2

M.S.R= M.S.R=
Violet V.C= V.C=
T.R= T.R=

Blue M.S.R= M.S.R=

V.C= V.C=
T.R= T.R=

M.S.R= M.S.R=
V.C= V.C=
Green T.R= T.R=

M.S.R= M.S.R=
Yellow 1 V.C= V.C=
T.R= T.R=

M.S.R= M.S.R=
Yellow 2 V.C= V.C=
T.R= T.R=

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Precautions

1. The ruled surface of the grating should never be touched.

2. The readings on both the verniers should be noted.
3. The prism table should be properly leveled before keeping the grating in the grating stand.
4. The prism table should not be disturbed after placing the grating in the normal position

Calculations

Result

The wave lengths of a given light using diffraction grating with normal incidence method are

λv= cm
λB= cm
λG= cm
λY1 = cm
λY2 = cm

Signature of the Faculty

17
 THICKNESS OF THIN OBJECT BY WEDGE METHOD Experiment No:
Date:

Aim
Determination of thickness of thin object by wedge method.
Apparatus
Two optically plane glass plates of same size, wooden frame, a piece of black paper, reading lens,
travelling microscope, reflecting glass plate, a wire of small thickness and a retard stand
Formula
𝜆𝑙
d= cm
2𝛽
Where d = thickness or diameter of the wire to be determined
β = Fringe width, λ = wavelength of the light used (sodium) = 5893X10 -8 cm, l = distance between the
point of contact of the glass plates and axis of the thin wire fixed in between them.
Description
The experimental arrangement is as shown in fig. Take two optically plane glass plates and then clean
them with a piece of cloth. Fix the wire whose thickness is to be determined between the two glass plates
in such away that the two glass plates touch at one end and separated at the other end. A thin film of air
or wedge shaped film will be formed between the two glass plates. The thickness of the air film or wedge
gradually increases from the point of contact of the two glass plates towards the other end. Now, place
this set on the wooden frame whose lower surface is covered with black paper. Light from a
monochromatic source S (sodium) is allowed to incident normally on the combination after partially
reflected a glass plate G which is inclined at an angle of 45 0 with the horizontal. The rays reflected at the
lower surface of the upper surface of the plate and partly from the top surface of the lower plate interfere
and produce interference fringes. As these two rays are derived from the same incident ray and hence
travelled over different paths, they are in a condition to produce interference fringes. The locus of all the
points having the same thickness of air film is as observed, which can be viewed through a microscope
held vertically above the centre of fringe system.
Procedure
Illuminate the wedge shaped film by sodium lamp. Adjust the glass plate G, until the inclination
0
is 45 with the horizontal, such that the light from the source S, after reflection from G incident normally
on the air-film. Focus the microscope vertically above the fringe system and adjusts the cross wires so
that the fringes are clearly seen. Move the microscope horizontally and adjust its position so that the
vertical cross-wire coincides with one of the fringes say, first fringe (near the point of contact).
Note the main scale reading and vernier coincidence of that fringe. Find the total reading. By counting
the number of fringes, move the microscope away from the point of contact of the glass plates and adjust
the microscope so that the vertical cross-wire coincides with the 3rdfringe. Then, note the M.S.R and V.C.

18
Find the total reading. Repeat the Experiment and note the observations for the 5th, 6th (r3), 8th (r4), and
10th (r5) fringe. While taking the observations see that the microscope is moved always in the same
direction to avoid back-lash error. Note the readings in the table. The difference between the two readings
gives the width of 5 fringes. From this, find the width of one fringe β. Measure the distance between the
point of contact of the two glass plates and the wire i.e., L. The thickness d of the given wire can be
calculated by substituting the values of λ, L and β formula.

Observations
Length of the wedge L = cm
Wave length of light  = 5893x10 cm
-8

S.No Fringe Microscope Fringe Microscope Width of 5 Fringe

Number reading Number reading fringes width
‘a’ cm ‘b’ cm C = a~b cm  = C/5
cm
1 1 6 1
2 3 8 2

3 5 10 3
Average width of one fringe, β = (  1 +  2 +  3 )/3 = cm
Precautions
1. The glass plates should be thin and optically plane
2. The glass plates should be cleaned with methylated spirit and then to be wiped with clean cloth.
3. The wire used should be thin and uniform without kinks.
4. The vertical cross-wire should be made to coincide with the bright fringe.
5. The travelling microscope should be moved in one direction only to avoid back-lash error.

19
Calculations

Result

Thickness of the given wire is d = cm

Signature of the Faculty

20
 Magnetic field along the axis of a current carrying circular coil by Experiment No:
Stewart & Gee’s Method Date:
method.

Aim
Magnetic field along the axis of a current carrying circular coil by Stewart & Gee’s Method

Apparatus

Stewart Gee type galvanometer, battery, plug key, commutator, rheostat

Circuit Diagram

Description

Stewart and Gee galvanometer is shown in the figure. Its construction resembles that of tangent
galvanometer and deflection magnetometer. It consists of a circular coil in a vertical plane fixed to a
horizontal bench at its middle point. The ends of the coil are connected to binding screws. A magnetic
compass box is arranged such that it can be slided along a horizontal scale passing through the centre of
the coil. The length of the scale is perpendicular to the plane of the coil. The compass box consists of a
short magnetic needle and a long aluminum pointer attached at is midpoint perpendicular to it and they
are pivoted at the centre of a horizontal circular scale graduated in diagrams. The circular scale consists
of four quadrates each of which measures angles from 0 0 to 900. A plane mirror is provided below the
pointer so the deflections can be observer without parallax.

Procedure

The circuit is constructed as shown in fig. the primary adjustments of the instrument are made. The coil
of the instrument is set along the magnetic meridian. The aluminum pointer is made to read 0 0-00 with no
current. The ends of the coil are connected to the commutator and though it to battery, rheostat and

21
ammeter. When the circuit is closed with plug key, a current flows through the circular coil. A magnetic
field is produced on the axis of the coil. The magnetic needle in the compass is subjected to the horizontal
component earth’s magnetic field (H) and magnetic field (B) due to the circular coil carrying current.
Those two magnetic fields are acting at right angles to each other. The magnetic needle is deflected
through an angle θ from the direction of (H) the horizontal component of earth’s magnetic field.

The current in the circuit in the circuit is adjusted such that the deflection lies between 30 0and 600 using
the rheostat. The compass box is displaced by certain distance along the horizontal scale and the deflection
of the needle is measured at every distance by reading both ends of the pointer. Let the readings be θ1 and
θ2. The readings θ3 and θ4 are observed after reversing the direction of current. The experiment is repeated
for different distances at equal intervals on one side and centre and also do the same on other side of the
coil and readings are tabulated and determine the average θ and tan θ for each distance. A graph is drawn
with tan θ along y-axis and distance x from the centre of the coil along x-axis. it is shown in graph. This
graph shows the variation of magnetic field along the axis of coil and the magnetic field is maximum at
the centre of coil.

Position Distance of Deflection

of compass from
compass centre of coil θ1 θ2 θ3 θ4 Average Tan θ
X θ = (θ1+ θ2+ θ3+ θ4)/4
cm

Left

Centre 0

Right

22
Graph :

Precautions

1. Galvanometer should not be disturbed after making primary adjustments

2. The deflections should be observed without parallax

3. Other magnetic and electronic objects should be kept away from the coil.

Result

Studied the variation of Magnetic field along the axis of a current carrying circular coil by using Stewart & Gee’s
galvanometer.

Signature of the Faculty

23
 THERMISTOR Experiment No:
Date:

Aim

To draw the resistance- temperature characteristics and to determine the thermo - electric coefficient of
thermistor

Apparatus

Thermistor, voltmeter, multimeter, oil bath arrangement

Circuit Diagram

Theory

A thermistor is a type of resistor whose resistance strongly depends on temperature. The word thermistor
is a combination of words “thermal” and “resistor”. A thermistor is a temperature sensing element
composed of sintered semiconductor material and sometimes mixture of metallic oxides such as Mn, Ni,
Co, Cu and Fe, which exhibits a large change in resistance proportional to a small change in temperature.
Pure metals have positive temperature coefficient of resistance, alloys have nearly equal zero temperature
coefficient of resistance and semiconductors have negative temperature coefficient of resistance.

Thermistors can be classified into two types: Positive temperature coefficient (PTC) thermistor-
resistance increase with increase in temperature. Negative temperature coefficient (NTC) thermistor-
resistance decrease with increase in temperature. The thermistor exhibits a highly non-linear characteristic
of resistance vs. temperature. PTC thermistors can be used as heating elements in small temperature-
controlled ovens. NTC thermistors can be used as inrush current limiting devices in power supply circuits.
Inrush current refers to maximum, instantaneous input current drawn by an electrical device when first

24
turned on. Thermistors are available in variety of sizes and shapes; smallest in size are the beads with a
diameter of 0.15mm to 1.25mm.

There are two fundamental ways to change the temperature of thermistor internally or externally. The
temperature of thermistor can be changed externally by changing the temperature of surrounding media
and internally by self-heating resulting from a current flowing through the device. The resistance of a
thermistor varies with temperature, according to the relation
R= AeB/T ------------------(1)

Where A and B are constant characteristics of the thermistor used, and T is the absolute temperature.
Taking logarithm on both sides
loge R = loge A+B/T --------(2)

2.303 log10 R=2.303 log10 A+0.4343B/T -------(3)

log10 A = log10 R- 0.4343B/T -------------(4)

𝑹𝟐−𝑹𝟏
α= / oC
𝑹 𝟏 𝑻𝟐 − 𝑹 𝟐 𝑻𝟏

Procedure

1. Connections are made as shown in the figure.

2. Place the thermistor in an oil bath using the heating arrangement.

3. Turn on the power supply and fix to a constant voltage.

4. Note the current readings using a digital multi meter or a milliammeter.

5. Corresponding resistance is found, using equation R = V/I

6. Vary the temperature of the oil bath using the heating arrangement.

7. Note the current readings at regular intervals of temperatures.

8. Corresponding resistances R is found using the same equation.

25
Graph

A graph is drawn taking temperature in ( oC) on the x-axis and resistance on the Y-axis.

Observations

Voltage =

Resistance
S.No Temperature Current R = V/I
(oC) (mA) (KΩ)

Calculations

26
Precautions

1. While taking the observations in heating and cooling parts of the experiment, temperatures should
be noted carefully.
2. The connections should be properly made without loose contacts.

Result

The temperature-resistance characteristics of a thermistor are drawn and determined the thermo electric
coefficient  = /o C

Signature of the Faculty

27
 PLANCK’S CONSTANT Experiment No:
Date:

Aim:

To determine the Planck’s constant ‘h’ from the stopping voltages measured of different.

Apparatus:

Photo emission cell mounted in a black iron bar provided with a wide slit and a filter holding stand, DC
power supply with two digital meters (0-200NA,0-2v), three set of filters and variable light source.

Principle:

This experiment is based on the principle of photo electric effect

Photo Electric Effect:

When a light of suitable frequency falls on the some metal surface electrons are ejected from the surface
without any delay. This effect is called photoelectric effect and the liberated electrons are called
photoelectrons.
Laws of Photo electric emission:
• There is no time lag between arrival of bottom and emission of electron
• Photocurrent increases with increase of intensity radiation and independent of frequency of
radiation
• Stopping potential increases with increase of frequency of radiation independent of intensity of
radiation
Formula:
The Planck’s constant is given by the formula,

𝑒(V1~V2)λ1λ2
ℎ= Js
C (λ1~λ2)

where ‘𝑒’ 𝑖𝑠 𝐶ℎ𝑎𝑟𝑔𝑒 𝑜𝑓 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 = 1.6 × 10−19 𝐶

‘𝐶’ 𝑖𝑠 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 = 3 × 108 𝑚/𝑠

𝑉1𝑎𝑛𝑑 𝑉2 𝑎𝑟𝑒 𝑠𝑡𝑜𝑝𝑝𝑖𝑛𝑔 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙𝑠 𝑜𝑓 𝑎𝑛𝑦 𝑡𝑤𝑜 𝑓𝑖𝑙𝑡𝑒𝑟𝑠 𝑎𝑛𝑑 𝑡ℎ𝑒𝑖𝑟

𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ𝑠 𝑎𝑟𝑒 𝜆1 𝑎𝑛𝑑 𝜆2

28
Circuit Diagram:

Theory:

We know that according to photo electric effect, when the light of suitable frequency falls on some
materials called photo sensitive materials like alkali materials, electrons are ejected from the material
without any time delay this effect is called photoelectric effect and the liberated electrons are called
photoelectrons. This can be explained on the basis of Einstein theory as follows. According to Max
Planck’s quantum theory, light energy from light source is emitted in terms of discrete packets of having
the value integral multiple of ‘h𝜗’. This packet of energy can also treat it as particle or photon coming
from light source.

Hence showering up light rays onto a material can be treated as showering of particles or photons coming
from light source these incidents photons transfer their energy of photons is used to liberate in the electrons
from metal atom and remaining energy is event to the same electron in the form of kinetic energy. This
can be expressed mathematically as

ℎ𝜗 = ℎ𝜗0 + 𝑚𝑣2

The above expression is also called Einstein’s photo electric Equation. Here ℎ𝜗0 is called the Work
function of that metal. By virtue of their Kinetic energy possessed, the liberated photo electrons in
photocell are able to reach anode and produce some photo current in circuit, even the absence of potential
difference applied (i.e at V=0). With the increase of positive potential given to anode, more and more
number of electrons is collected by anode, and thereby photo current increases linearly up some positive
potential and becomes constant at high value of potentials. This is because, at high value of potentials, all
the produced photo electrons at one particular intensity of light, are collected by anode. When intensity
of light Source increased, more photo current is produced in the circuit. When negative potential is to
anode because of repulsion number of photo electrons reaching towards anode decreases and leads to
decrease in photocurrent with increase of negative potential as shown in figure 2. At a particular negative
potential photo current in the circuit becomes to zero called stopping potential. At stopping potential, the
photoelectron having maximum kinetic energy is experiencing maximum repulsion from negative

29
potential, and hence unable to reach the anode. Due to this photocurrent is zero in the circuit. Stopping
potential depends upon kinetic energy of photoelectron, which intern depends upon photo energy or
frequency of radiation. Hence stopping potential increases with increases frequency of radiation, and
independent of intensity of radiation.

𝐾. 𝐸𝑚𝑎𝑥 = 𝑚𝑣 max2 = ℎ𝜗

ℎ𝜗1 = ℎ𝜙 + 𝑒𝑉1 − − − − − − − (1)

ℎ𝜗2 = ℎ𝜙 + 𝑒𝑉2 − − − − − − − (2)

from eq. (1) and (2) we can write

𝑒(V1~V2)
ℎ=
(𝜈1 ~𝜈2 )
𝑐
we know 𝜈=
𝜆
therefore

𝑒(V1~V2)λ1λ2
ℎ= Js
C (λ1~λ2)

Procedure

1. Switch on the unit. Now set the digital A reading to zero with the help of potentiometer marked with
zero adjust.
2. The circuit connections are made as shown in diagram (Fig-1). Be careful about the polarity shown in
diagram.
3. A light source is arranged. The light is allowed to fall on the tube. The distance between tube and
light source is adjusted such that there is a deflection of about 50 A-80A in digital micro ammeter.
Now a suitable filter (say green) of known wave length is placed in the path of light (in the slit
provided) say it is with wave length 𝜆2 .
4. A reading is observed in the digital micro ammeter. This deflection corresponds to the zero anode
potential.
5. A small negative voltage is applied on the anode. This voltage is recorded with the help of digital
voltmeter provided (2.0 volts range).
6. The negative anode potential is gradually increased in steps and each time corresponding reading
is noted till the micro-ammeter reading reduces to zero and this is stopping potential V 2
corresponding to filter with wave length 𝜆2 .
7. The experiment is repeated after replacing the green filter with orange and blue filters Say with
wave length 𝜆1 𝑎𝑛𝑑 𝜆3 respectively and stopping potential V 1 and V3 are noted.

30
8. Taking negative anode potential on x-axis and corresponding deflections in micro-ammeter on y-
axis, graphs are plotted for different filters.
9. By using above values Planck’s Constant ‘h’ is calculated by the formula given. Standard values
of e & c and wave length of standard filters are given below.

Tabular form:

S.No Colour of the filter Wavelength of the colour Stopping Potential

(V)
(𝝀) ‘m’

1 Orange 6125x10-10 m
2 Green 5645x10-10 m
3 Blue 5265.5x10-10 m

Calculation:

𝑒 = 1.6 × 10−19 𝐶

c = 3 × 108 𝑚/𝑠

V1 = 𝝀1 =

V2 = 𝝀2 =

ⅇ(𝐕𝟏~𝐕𝟐)𝛌𝟏𝛌𝟐
𝒉= Js
𝐂 (𝛌𝟏~𝛌𝟐)

Wave length of orange filter 𝜆1 = ̅ 2% meter.

612.5x10-10+

Wave length of orange filter 𝜆2 = ̅ 2% meter.

5645x10-10+

Wave length of orange filter 𝜆3 = ̅ 2% meter.

5265.5x10-10+

31
Precautions

1. Make sure the photocell, light source, and filter are aligned perfectly.

2. Measure the stopping potential by adjusting the anode potential in small steps.

3. Rotate all the knobs very slowly.

4. Handle the filters with utmost care and avoid touching their surfaces.

Result:

The Planck’s constant is found to be h = ………………………………. Js

Standard value of h is known to be 6.626×10 -34 J-s

Signature of the Faculty

32
 TORSIONAL PENDULUM Experiment No:
Date:
Aim

To determine the modulus of rigidity of the material of the given wire by dynamical method using
torsional pendulum.

Apparatus

Torsional pendulum, stopwatch, a vertical pointer, screw gauge and vernier calipers.

Description

The torsional pendulum consists of a uniform metal disc suspended by means of a wire. The upper end
of the wire is gripped in a chuck fixed to a wall bracket (or) held tightly in a clamp and the lower end of
the wire is gripped in another chuck fixed at the centre of the disc, so that the disc rotates about the axis
of the wire

Theory

When the disc is turned through a small angle in the horizontal plane and released, it executes torsional
oscillations about the wire as axis. The period of oscillation is given by

T = 2 I
C ……………….. (1)

Where ‘ I ’ is the moment of inertia of the disc above the axis of

rotation and ‘c’ is the couple per unit twist of the wire.

If ‘ l ’ is the length of the wire under tension and ‘r’ is its radius then

 r4
C= 2l ………………… (2)

Where ‘  ’ is the modulus of rigidity of the material of the wire

Squaring (1) and then substituting the value of ‘C’ form (2) then we get

8 I l
= .
r 4 T 2 ………………. (3)

But the moment of inertia ‘ I ’ of the circular disc about the axis of rotation is given by

33
 I = MR 2 / 2 ………………….. (4)

Where ‘M’ is the mass of the disc and ‘R’ is its radius

Procedure

The kinks, if any in the wire are removed and the given disc is suspended as shown in the figure.
The length (l) of the wire between the chucks is adjusted to a convenient value, a fine chalk mark is
made on the curved edge of the disc and vertical pointers is placed in front of the disc against the chalk
mark. This helps us to count the number of oscillations. The disc is turned through a small angle in the
horizontal plane and released. By means of a stop-watch the time for 10 oscillations is noted twice and
the mean time is calculated. The time period ‘T’ is then found. The experiment is repeated for different
values of ‘ l ’ and in each case the time period is determined.

Graph

A graph is drawn with a ‘ l ’ along x-axis and ‘T2’ along the y-axis. The graph is a straight line
passing through the origin and the mean value of ( l /T2) is obtained from the graph. The radius ‘r’ of the
wire is determined with Screw-Gauge by measuring the diameter at three different places, taking two
readings at each place in two perpendicular directions. The mean ‘M’ of the disc is found with a rough
balance and its mean radius is obtained by measuring its diameter at three different places by means of
vernier calipers. The moment of inertia of the disc about the axis of the wire is calculated by using the
2
I = MR
formula 2

Model Graph

Observations:

To determine radius of the disc R:

Least Count of vernier calipers: 0.01 cm

34
 S.No. M.S.R Vernier Coincidence Diameter of the disc

a cm b D = a+(bX0.01) cm

Radius of the disc R = D/2 = cm

To determine the radius of the wire r:

Least Count of the Screw Guage = 0.001 cm

Error = Correction =

S.No Pitch Scale Head Scale Correction b = nXL.C

Reading Reading
n C = (a+b) cm
a

Radius of the wire (r) = C/2 = cm

S.NO Length (L) Time for 10 oscillations Period T2

Cm Trial -1 Trial-2 Mean T = t/10 sec Sec2

1 40

2 50

3 60

4 70

5 80

35
Calculations

Precautions

1. The wire should be free from kinks.

2. The radius of the wire should be determined accurately as it occurs in the fourth power in the
formula.

3. The disc should only rotate about the axis of the wire and should not oscillate like a simple
pendulum

Result

The rigidity modulus of the material of the given wire ƞ= Dynes/cm 2

Signature of the faculty

36
 COMPOUND PENDULUM Experiment No:
Date:

Aim:

Determination of Acceleration due to gravity (g) and Radius of gyration(k) using a compound
pendulum.

Apparatus:

Compound Pendulum, stop watch, knife edge, meter scale and a Telescope, wax, pin.

Formula:
1.Acceleration due to Gravity g= 4π2 (l/T2) =
2. Radius of gyration K = √ℎ1 ℎ2 in cm

Description: It consists of a rectangular metal bar having number of holes drilled along its length at equal
distances. It is suspended by a knife edge passing through one of the holes. Such an arrangement is called
compound pendulum. As its length is 90cm, its c.g. lies at 45cm. Knife edge is placed on a glass plate
kept on wall bracket so that pendulum oscillates freely. A pin is fixed by wax at the lower end of the
pendulum bar. The pin is viewed through a telescope lying in front of it for counting oscillations.

Theory: As length of pendulum from one end L is increased from 10cm to 40cm, time period T first
decreases becomes minimum and then increases. The pendulum bar is reversed. If L is increased from
50cm to 80cm, again T first decreases, becomes minimum and then increases. From L-T graph, equivalent
length of simple pendulum l is found. Thus, g is calculated. Also, Radius of gyration k is found.

Principle: When a freely suspended rectangular bar with holes is pulled to a side and released, it executes
oscillations and undergoes linear simple harmonic motion. From L-T graph, equivalent length of simple
pendulum l is found and g is calculated. Also, radius of gyration k is determined.

Procedure: To start with L is fixed as 5 cm from one end and pendulum is oscillated. Time for 10
oscillations t is noted by a stop watch from which Time period T is found. L is increased in steps of 5cm
up to 45cm. Corresponding Time periods are noted in the Table. Now the pendulum bar is reversed. By
changing lengths, from 55cm to 95cm corresponding Time periods are again found and noted in Table.
Even after reversing the pendulum bar, length must be measured from the same end only.

37
Tabular Form

Distance of knife Time for 10 oscillations (sec) Time Period

S.No edge from one end T = t/10
l (cm) Trial 1 Trial 2 Mean (sec)
‘t’ sec
1 5
2 10
3 15
4 20
5 25
6 30
7 35
8 40
9 45
10 50
11 55
12 60
13 65
14 70
15 75
16 80
17 85
18 90
19 95

From Graph

Equivalent Length (𝑙)

Mean 𝑇2
AC + BD Time
S. No: 𝑙/𝑇2
AC BD 𝑙= Period
2 T (sec)
(cm)

1.

38
For Radius of Gyration

Sl.no 𝐴𝐷 = ℎ1 𝐵𝐶 = ℎ2 𝐾 = √ℎ1 ℎ2

Graph: Draw a graph with Time period (T) along the Y-axis and distance of point of suspension
(l) along X – axis. Two symmetrical curves are obtained as shown in the figure.

Calculations:

1.Acceleration due to Gravity g= 4π2 (l/T2) = cm/sec2

2. Radius of gyration K = √ℎ1 ℎ2 = cm

Precautions:

1. The pendulum must be oscillated in the vertical plane with small amplitude without wobbling.
2. The knife edge should be horizontal.
3. Lengths must be measured from one end of the bar even after reversing the pendulum bar.

Result:

1.Acceleration due to Gravity g= 4π2 (l/T2) = cm/sec2

2. Radius of gyration K = √ℎ1 ℎ2 = cm

Signature of the Faculty

39
 DISPERSIVE POWER OF THE PRISM Experiment No:
Date:

Aim

To determine the Dispersive power of prism by minimum deviation method.

Apparatus

Spectrometer, mercury vapour lamp, reading lens, spirit level, prism and hand lamp.

Formula

The dispersive power of material of the prism for two colors is given by

ω = µ1~ µ2

where µ1 and µ2 are refractive indices of two colors and

µ1+ µ2
µ =
2

The refractive index of material of the prism is given by

𝑨+𝑫
𝐬𝐢𝐧( )
𝟐
µ= 𝑨
𝐬𝐢𝐧( 𝟐 )

Description

A spectrometer is an optical instrument used to produce and study various types of spectra. The essential
components of a spectrometer are

(i) Collimator

(ii) Prism Table

(iii) Telescope.

(iv) Collimator

The collimator is a device to produce a parallel beam of light. The collimator consists of two coaxial cylindrical
metal tubes one sliding into the other. A convex lens is fitted to one end of one tube and an adjustable vertical slit
(rectangular) is fixed to the outer end of the other tube. The width of the slit can be adjusted by means of a screw
S1. The distance between the slit and the lens can be altered by a rack and pinion screw S 2. The collimator is fixed
to the base of the instrument, with its axis perpendicular to the axis of rotation 0 of the prism table. When the slit,

40
which is in the focal plane of the lens is illuminated with a source of light (i.e., when the length of the collimator is
equal to the focal length of the lens) the rays of light emerging out of the lens will be parallel (Fig. 1).

(ii) Prism table

It consists of two circular metal plates which are joined together by means of three levelling screws and springs (x,
y, z), with the help of which it can be made perfectly horizontal. On the surface of the upper disc are drawn
concentric circles and also straight lines parallel to the line joining two of the levelling screws. The prism table can
be raised or lowered or can be fixed at any desired height by means of a screw S 3 and this can be fixed to the vernier
table. Slow motion of the vernier table along with the prism table can be made by a tangential screw provided at the
base of the instrument. The axis of rotation of the prism table passes through the centre of the circular scale, called
the main scale which is graduated in half degrees. Readings can be taken with the help of two diametrically opposite
verniers V1 and V2, which are provided on a vernier table. This is to minimise errors due to non-coincidence of the
centre of the circular scale with the axis of rotation.

(iii) Telescope

The telescope is of astronomical type, which is used to receive the parallel beam of light. It consists of two coaxial
cylindrical hollow metal tubes, one sliding inside the other. An objective (an achromatic combination of lenses or
convex lens) is fixed at the inner side of the outer tube, which is towards the prism table. The inner tube is fitted
with a third tube carrying cross-wires and an eye-piece. The distance between the objective and eye-piece can be

41
adjusted by rack and pinion screw S6, while that between the cross-wire and the eye-piece can be adjusted by moving
it in or out by hand. The telescope is fixed to a vertical support and can be rotated (about the vertical axis of rotation
of the prism table) or fixed at any desired position with a position S5. Slow motion of the telescope can be made
with a tangential screw S7. The position of the telescope can be read on a circular scale fixed to it with the help of
two diametrically opposite verniers. When parallel rays from the collimator falls on the objective, the image of the
slit is formed in the focal plane of the eye-piece where cross- wires are fixed.

To determine the least count of the vernier of the spectrometer

The circular scale is graduated into half degrees i.e. from 0° to 360°. One degree is divided into two divisions. The
vernier scale is divided into 30 equal divisions.

On the circular scale, 2 divisions =1

Value of one main scale division (1 M.S.D), S =30 |

Total number of divisions on the vernier,N= 30

30′
Least count of the vernier of the spectrometer, L.C =S/N= = 1’
30

Procedure

Determination of the angle of minimum deviation D

Now turn the prism on the prism table such that light from the collimator is incident on one of the refracting
surfaces, say AB. It emerges out of the second face AC after refraction through the prism (Fig. 1.7). A
line spectrum which consists of number of lines can be seen through the telescope by turning it.
(Spectrometer can be covered with black cloth to cut extraneous light such that the spectrum is more
clear). While looking through the telescope rotate the prism table slowly in one direction following the
spectral lines. We observe spectral lines moving towards the direct reading position of the telescope. As
we continue to rotate the prism table in the same direction, in one particular position, the spectral lines
suddenly start retracing their path (or turn back). The particular position of the spectral line where it begins
to retrace its path is known as the minimum deviation position for that particular line (λ). The

42
corresponding angle of deviation is called angle of minimum deviation. When the
spectrum is about to retrace its path, then clamp the prism table and adjust the
position of the telescope with the slow motion screw until the vertical cross-wire
coincides with say, the violet line of the spectrum. Then, note the main scale

reading and vernier coincidence on both the verniers (V1 and V2). Find the total
reading d, on each vernier. Now remove the prism from the prism table, release
the telescope and turn it opposite to collimator. See the direct image of the slit
through the telescope and adjust its position with slow motion screw until the
vertical cross-wire coincides with the image of the slit. Note the M.S.R and VC
on both the verniers. Find the total reading d2. The difference between the reading
in the minimum deviation position d1, and the reading in the direct image position
d2, on the vernier 1 gives the angle of minimum deviation D for that violet line.
Similarly, the difference between the reading in the minimum deviation position
and the reading in the direct image position on the vernier 2 gives the angle of minimum deviation D, for
the same line of the spectrum. Then the mean angle of minimum deviation D is obtained from the relation,
D1 + D2
D=
2

Repeat the experiment for other spectral lines and in each case find the mean angle of minimum deviation
for each line. The refractive index µof the material of the prism for each wavelength (line) can be
calculated using the relation 1.2. The dispersive power ω of the material of the prism for any two colors
can be obtained using the relation 1.1. The results are to be tabulated

OBSERVATIONS

The angle of prism A= 60

Direct image reading (without prism)

V1 =

V2 =

43
Colour Vernier Telescope Reading in the Angle of Mean 𝑨+𝑫
𝐬𝐢𝐧( )
𝟐
of the minimum deviation position min. angle of µ = 𝑨
𝐬𝐢𝐧( 𝟐 )
spectral Deviation minimum
line M.S.R V.C Total reading Deviation
D = d1 ~
a n d1 = a + (n x d2 𝐃𝟏 + 𝐃𝟐
D=
L.C) 𝟐

V1

Violet V2

V1

Blue V2

V1

Green V2

V1

Yellow V2

Red V1

V2

Calculations

44
Precaution

1. Take the readings without any parallax errors

2. The focus should be at the edge of green and blue rays

Result:

Dispersive power of prism ω =

Signature of faculty

45
 MEASUREMENT OF WAVELENGTH OF LASER SOURCE - Experiment No:
DIFFRACTION GRATING Date:

Aim

To determine the wavelength of given laser light using the diffraction grating.

Apparatus

He-Ne or semiconductor laser source, a transmission grating, an optical bench, screen, meter scale

Theory

The wavelength of laser light (LASER– Light Amplification by Stimulated Emission of Radiation) is
determined by using the grating. Diffraction means the bending of light rays around the edges of the
obstacle. To get the diffraction pattern, spacing between the lines on the grating should be of the order of
wavelength of light used. The laser light is allowed to fall on the grating and it gets diffracted. The
diffracted rays will form alternate bright and dark fringes and by using Bragg’s equation, the wavelength
of laser light is determined.

Procedure

The grating is placed between the laser source and the screen. The orientation of the laser in the above set
up is adjusted till a bright spot is seen on the screen. This position corresponds to the central maximum,
and this position is marked on the screen. Next, the screen is moved towards or away from the grating till
clear light spots are seen on either side of the central maximum. These light spots on either side of the
central maximum correspond to images of different orders of the spectrum. The nearest spots to either

46
side of the central maximum correspond to the image of first order, and the next will correspond to the
images of second order and so on. The positions of these spots are also marked on the screen. The distance
between the grating and the screen is measured. Let it be ‘d’, the distance between the central maximum
and first, second, third maximum is measured and so on. The same procedure is repeated on the other side
of the central maximum. The readings are tabulated and calculations are done.

OBSERVATION
To find the Wavelength of Laser Source

Number of lines per meter on grating N =

Distance between Order Distance between central

𝟏 𝐗𝐧
grating and n maximum and diffracted λ= [ ] 𝒄𝒎
𝒏𝑵 √𝒙𝟐𝒏+ 𝑫𝟐
screen (D) cm image Mean
Xn
Left Right
cm

Calculations

Result:

The wavelength of the given laser is λ = cm

47
 DIELECTRIC CONSTANT Exp. No:

Date:

Aim: Measurement of Dielectric Constant of different materials

Apparatus: Dielectric Constant Measurement Trainer, Solid Samples, Mains Cord, Patch Cord

Procedure

1. Connect the Mains Cord to the trainer & switch ‘On’ the rocker switch.

2. Now rotate the variable resistance knob fully in clockwise direction.

3. Connect variable capacitor to RF output on the trainer.

4. Change the value of capacitance for which maximum value of current is obtained that is the condition
of resonance.

5. Note the value of capacitance. Let it be C1.

6. Place the dielectric sample between the plates of test capacitor such that the dielectric sample just
touches both the plats with the help of adjusting screw.

7. Now connect the Test Capacitor with dielectric sample with the help of patch cords across the Test
Capacitor (marked) on the trainer.

8. Now reduce the value of variable capacitor to obtain the condition of resonance.

9. Note the value of capacitance. Let it be C2.

10. Subtract C1and C2 to determine the value of test capacitance that is C here.

11. Now carefully remove the dielectric material from the test capacitor without changing the distance
between the plates.

12. Now determine the distance between both the plates. Note: Take the help of vernier caliper for better
result.

13. Determine the value of area of any one plate of test capacitor that is A by using the formula (Length
x Breath)

Now calculate the value of Dielectric Constant of given material by following formula

48
Where, K = Dielectric Constant A = Area of plate d = Distance between two plates C = Capacitance ε0 =
Permittivity of free space its value is ε o = 8.854×10−12 F m–1

15. Repeat the whole experiment for determining the dielectric constant of different material.

Observations:

1. Capacity of variable capacitor at resonance alone C 1 =______pf

2.Capacity of variable capacitor at resonance with text capacitor (with dielectric in it) C 2=_____pf

3.Capacity of variable capacitor at resonance with text capacitor (without dielectric in it) C3=_____pf

S.no Thickness of Value of variable capacitor at resonance when

dielectric Alone C 1 With test capacitor With test capacitor

material (bk. ( with dielectric in it) (without dielectric in it)

sheets) in mm C2 C3

1 3mm pf pf pf

2 4.5mm pf pf pf

3 6mm pf pf pf

4 7.5mm pf pf pf

Precautions:

1. Test capacitor plates should be tight when filled with dielectric material.

49
2. Three sheets are provided for solid dielectric one sheet is 1.5

3. By using all the three sheets thickness will be 7.5mm

Result:

Dielectric constant of Bakelite is .....................,

Dielectric constant of Teflon is .................

50
 BREWSTER'S LAW

Aim:

To verify the Brewster's law and to find the Brewster's angle.

Introduction:

An ordinary light source consists of a very large number of randomly oriented atomic emitters.
They radiate polarized wavetrains for roughly 10 -8 s. These wavetrains combine to form a single resultant
polarized wave which persists for a short time, not more than 10 -8 s. Since natural light composes of a
large number of rapidly varying succession of the different polarization states it is said to be an unpolarised
or randomly polarized light.

The natural light can be expressed in terms of two arbitrary, incoherent, orthogonal, linearly polarized
waves of equal amplitude. Figure (a) shows randomly polarized natural light and figure (b) shows the
splitting at 50% horizontal and 50% vertical states.

A light is said to be a plane polarised light, if all the vibrations are confined to a single plane. Consider an
unpolarised light incidents on a transparent surface. If the angle of incidence is equal to a particular angle
of incidence, the reflected light produced will be completely plane polarized. This particular angle is
called the Brewster’s angle or the polarizing angle B.

Sir David Brewster, in 1892, found that the maximum polarization of the reflected ray occurs when the
reflected ray is perpendicular to the refracted ray. This is called the Brewster’s law.

51
Brewster’s equation:

Where, μ2 is the refractive index of the reflecting surface and μ 1 is the refractive index of the surrounding
medium. The refracted ray so produced will be partially polarized. As the refractive index changes the
polarizing angle differs but it is independent of the wavelength of light used.

Performing the Simulation:

Drag the components from the right panel and place them correctly in the optic bench.

Start : This button enables the user to start the experiment.

Side view/Top view : Using this, different views of the experimental arrangement can be seen.

Choose light : Using this combo box, one can select different lasers.

Choose medium : The medium of different refractive index can be selected using this combo box.

Choose material : Different materials can be selected using this combo box.

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Switch on light : The user can make the laser source ON/OFF using this button.

Angle of the polariser : Using this slider, one can change the angle of the polariser from zero to 360
degrees.

Angle of incidence : This slider helps one to change the angle of incidence, which can be varied from
zero to 360 degrees.

Reset : The experimental arrangement can be reset using this button.

Self evaluation

1. Light waves can be polarised. This provides evidence that light waves are what kind of waves?
(a) Stationary waves (b) Monochromatic (c) Longitudinal waves Transverse waves
2. How is light reflected at the polarising angle?
(a)Polarised parallel to the reflecting surface (b)Polarised parpendicular to the
reflecting surface (c) Polarised parallel and perpendicular to the reflecting surface
(d)Polarised in the direction in which the wave is travelling
3. Which among the following shows the transverse wave nature of light?
(a) Diffraction of light through a single slit (b) Interference of light in a thin soap
film (c) Polarisation of light through selective absorption (d) Refraction of light
through a glass plate
4. Which among the following processes cannot be used to produce linearly polarised light?
(a) Scattering (b) Diffraction (c) Double refraction (d) Reflection
5. At Brewster's angle, the reflected light will be________.
(a)Linearly polarized (b) Partially polarized (c)Plane polarized (d) None of these

Assignment questions

1. Calculate the Brewster’s angle for crown glass in different medium (air, Helium, Hydrogen and
carbondioxide).
2. Calculate the Brewster's angle for light incidenting on a flint glass surface in different medium (air,
Helium, Hydrogen and carbondioxide).

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 BEAM DIVERGENCE AND SPOT SIZE
Aim:
To calculate the beam divergence and spot size of the given laser beam.

Laser:

The term LASER is the acronym for Light Amplification by Stimulated Emission of Radiation. It is a
mechanism for emitting electromagnetic radiation via the process of stimulated emission. The laser was
the first device capable of amplifying light waves themselves. The emitted laser light is a spatially
coherent, narrow low-divergence beam. When the waves(or photons) of a beam of light have the same
frequency, phase and direction, it is said to be coherent . There are lasers that emit a broad spectrum of
light, or emit different wavelengths of light simultaneously. According to the encyclopedia of laser
physics and technology, beam divergence of a laser beam is a measure for how fast the beam expands far
from the beam waist. A laser beam with a narrow beam divergence is greatly used to make laser pointer
devices. Generally, the beam divergence of laser beam is measured using beam profiler.

Lasers usually emit beams with a Gaussian profile. A Gaussian beam is a beam of electromagnetic
radiation whose transverse electric field and intensity (irradiance) distributions are described by Gaussian
functions.

For a Gaussian beam, the amplitude of the complex electric field is given by

where,
r - radial distance from the centre axis of the beam
z - axial distance from the beam's narrowest point
i - imaginary unit (for which i2 = − 1)
k - wave number (in radians per meter).
w(z) - radius at which the field amplitude drops to 1/e and field intensity to 1/e2 of their axial values,
respectively.
w(0) - waist size.
E0 = |E( 0,0) |
R(z) - radius of curvature of the beam's wavefronts
ζ(z) - Gouy phase shift. It is an extra contribution to the phase that is seen in beams which obey Gaussian
profiles.

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The corresponding time-averaged intensity (or irradiance) distribution is

where I0 = I(0,0) is the intensity at the center of the beam at its waist. The constant is defined as the
characteristic impedance of the medium through which the beam is propagating.
For vacuum,

Beam parameters:

Beam parameters govern the behaviour and geometry of a Gaussian beam. The important beam parameters
are described below.

Beam divergence:

The light emitted by a laser is confined to a rather narrow cone. But, when the beam propagates outward,
it slowly diverges or fans out. For an electromagnetic beam, beam divergence is the angular measure of
the increase in the radius or diameter with distance from the optical aperture as the beam emerges.

The divergence of a laser beam can be

calculated if the beam diameter d 1 and
d2 at two separate distances are known.
Let z1and z2 are the distances along the
laser axis, from the end of the laser to
points “1” and “2”.

Usually, divergence angle is taken as the full angle of opening of the beam. Then,

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Half of the divergence angle can be calculated as

where w1 and w2 are the radii of the beam at z1 and z2.

Like all electromagnetic beams, lasers are subject to divergence, which is measured in milliradians (mrad)
or degrees. For many applications, a lower-divergence beam is preferable.

Spot size:

Spot size is nothing but the radius of the beam itself. The irradiance of the beam decreases gradually at
the edges.

The distance across the center of the

beam for which the irradiance
(intensity) equals 1/e2 of the
2
maximum irradiance (1/e = 0.135) is
defined as the beam diameter. The
spot size (w) of the beam is defined as
the radial distance (radius) from
the center point of maximum
2
irradiance to the 1/e point.

Gaussian laser beams are said to be diffraction limited when their radial beam divergence is close to the
minimum possible value, which is given by

where λ is the wavelength of the given laser and w0 is the radius of the beam at the narrowest point, which
is termed as the beam waist.

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Performing the real lab:

• Arrange the laser and detector in an optical bench arrangement.

• The laser is switched on and is made to incident on the photodiode.

• Fix the distance, z between the detector and the laser source.

• By adjusting the micrometer of the detector, move the spot in the horizontal direction, from left to
right.

• Note the output current for each distance, x from the measuring device.

• Then the beam profile is plotted with the micrometer distance along the X-axis and intensity of
current along Y-axis. We will get a gaussian curve (see Fig.1).

Fig.1 beam profile of Laser beam divergence.

• The experiment is repeated for different detector distances.

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 • Note the points in the graph where the intensity equals 1/e2 of the maximum intensity, say it as
Ie (see Fig.1).

• Find the micrometer distance across the beam corresponding to these points ( B-A from the Fig.1)
for a pair of detector distances z 1 and z2. Half of this distance is noted as w1and w2.

• Then the divergence and spot size of the laser beam can be calculated from the equations.

Observation and calculation

To find the Least Count of Screw gauge

One pitchscale division ( n) = .............. mm
Number of divisions on head scale (m) = ...............
Least Count (L.C) = n/m = ......................
z1 = ....................... cm z2 = ................ cm

1/e2 of maximum intensity,Ie =................ mA 1/e2 of maximum intensity,Ie =................ mA

Diameter of the beam corresponds to I e, d1= Diameter of the beam corresponds to I e, d2=
..................mm ..................mm

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Divergence angle(Θ) = (d 2-d1)/(z2-z1) = ........................ mrad

Performing the simulator:

1. The experimental arrangement is shown in the simulator. A side view and top view of the set up
is given in the inset.

2. The start button enables the user to start the experiment.

3. From the combo box, select the desired laser source.

4. Then fix a detector distance, say 100 cm, using the slider Detector distance, z.

5. The z distance can be varied from 50 cm to 200 cm.

6. For a particular z distance, change the detector distance x, from minimum to maximum, using the
slider Detector distance, x. The micrometer distances and the corresponding output currents are
noted. The x distances can be read from the zoomed view of the micrometer and the current can
be note from the digital display of the output device.

7. Draw the graph and calculate the beam divergence and spot size using the steps given above.

8. Show graph button enables the user to view the beam profile.

9. Using the option Show result, one can verify the result obtained after doing the experiment.

Self Evaluation

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1) What is LASER?
(a) Light Amplification by Stimulated Emission of Radiation
(b) Light Amplitude by Stimulated Emission of Radiation
(c) Light Amplification by Stimulation Emission of Radiation
(d) Light Amplification and Stimulated Emission of Radiation
2) As distance increases, what happens to the intensity of the laser beam?
(a) Increases (b) Decreases (c) No change (d) Does not depend on distance
3) What is the minimum value of the spot size of a laser beam along the beam axis called?
(a) Confocal parameter (b) Rayleigh range (c) Beam waist (d) Beam width
4) The relationship between beam width and divergence is due to:
(a) Interference (b) Refraction (c) Diffraction (d) Dispersion
5) The constant 'eta' is the characteristic impedance of the medium in which the laser beam is propagating.
What is it's value for free space?
(a) 377 ohm (b) 277 ohm (c) 255 ohm(d) 355 ohm

Assignment

1. Define and explain beam divergence and spot size?

2. Find the spot size of the three laser beams provided in the simulator and comment.

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 Numerical Aperture of Optical Fiber
Aim:

To find the numerical aperture of a given optic fibre and hence to find its acceptance angle.

What is optic fibre?

Optical fibers are fine transparent glass or plastic fibers which can propagate light. They work under the
principle of total internal reflection from diametrically opposite walls. In this way light can be taken
anywhere because fibers have enough flexibility. This property makes them suitable for data
communication, design of fine endoscopes, micro sized microscopes etc. An optic fiber consists of a core
that is surrounded by a cladding which are normally made of silica glass or plastic. The core transmits
an optical signal while the cladding guides the light within the core. Since light is guided through the
fiber it is sometimes called an optical wave guide. The basic construction of an optic fiber is shown in
figure (1).

In order to understand the propagation of light through an optical fibre, consider the figure (2).
Consider a light ray (i) entering the core at a point A , travelling through the core until it reaches the core

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cladding boundary at point B. As long as the light ray intersects the core-cladding boundary at a
small angles, the ray will be reflected back in to the core to travel on to point C where the process of
reflection is repeated .ie., total internal reflection takes place. Total internal reflection occurs only when
the angle of incidence is greater than the critical angle. If a ray enters an optic fiber at a steep angle(ii),
when this ray intersects the core-cladding boundary, the angle of intersection is too large. So, reflection
back in to the core does not take place and the light ray is lost in the cladding. This means that to be guided
through an optic fibre, a light ray must enter the core with an angle less than a particular angle called the
acceptance angle of the fibre. A ray which enters the fiber with an angle greater than the acceptance angle
will be lost in the cladding.

Consider an optical fibre having a core of refractive index n 1 and cladding of refractive index n 2. let the
incident light makes an angle i with the core axis as shown in figure (3). Then the light gets refracted at
an angle θ and fall on the core-cladding interface at an angle where,
---------------------- (1)

By Snell’s law at the point of entrance of light in to the optical fiber we get,

-------------------- (2)

Where n0 is refractive index of medium outside the fiber. For air n 0 =1.

When light travels from core to cladding

it moves from denser to rarer medium and so it may be totally reflected back to the core medium

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if θ' exceeds the critical angle θ'c. The critical angle is that angle of incidence in denser medium (n1) for
which angle of refraction become 90°. Using Snell’s laws at core cladding interface,

or

----------------------- (3)

Therefore, for light to be propagated within the core of optical fiber as guided wave, the angle of incidence
at core-cladding interface should be greater than θ'c. As i increases, θ increases and so θ' decreases.
Therefore, there is maximum value of angle of incidence beyond which, it does not propagate rather it is
refracted in to cladding medium ( fig: 3(b)). This maximum value of i say i m is called maximum angle of
acceptance and n0 sin im is termed as the numerical aperture (NA).
From equation(2), acceptance and n0 sin im is termed as the numerical aperture (NA).
From equation(2),

From equation (2)

Therefore,

The significance of NA is that light entering in the cone of semi vertical angle i m only propagate through
the fibre. The higher the value of im or NA more is the light collected for propagation in the fibre.
Numerical aperture is thus considered as a light gathering capacity of an optical fibre.

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Numerical Aperture is defined as the Sine of half of the angle of fibre’s light acceptance cone. i.e. NA=
Sin θa where θa, is called acceptance cone angle.

Let the spot size of the beam at a distance d (distance between the fiber end and detector) as the radius of
the spot(r). Then,

------------------------ (4)

Procedure for simulator

Controls

Start button: To start the experiment.

Switch on: To switch on the Laser.
Select Fiber: To select the type of fiber used.
Select Laser: To select a different laser source.
Detector distance (Z): Use the slider to vary the distance between the source and detector. (ie toward the
fiber or away from the fiber.
Detector distance(x): Use the slider to change the detector distance i.e towards left or right w.r.t the fiber.
Show Graph: To Displays the graph.
Reset: To resets the experimental arrangement.

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 Preliminary Adjustment

• Drag and drop each apparatus in to the optical table as shown in the figure below.

Fig (4)
• Then Click “Start” button.
• Switch On (now you can see a spot in the middle of the detector)
• After that select the Fiber and Laser for performing the experiment from the control options.

To perform the experiment

• Set the detector distance Z (say 4mm). We referred the distance as “d” in our calculation.
• Vary the detector distance X by an order of 0.5mm, using the screw gauge (use up and down arrow
on the screw gauge to rotate it).
• Measure the detector reading from output unit and tabulate it.
• Plot the graph between X in x-axis and output reading in y-axis. See figure 5.
• Find the radius of the spot r, which is corresponding to Imax/2.71 (See the figure 5).

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 Fig (5)
• Then find the numerical aperture of the optic fiber using the equation (4).

Observation column
SL No. Screw gauge reading Distance
I µA
H.S.R P.S.R (X) mm

Calculations

Distance between the fiber and the detector, d = …………………………… m

Radius of the spot, r =……………………….. m

Numerical Aperture of the optic fiber, sin(θ) = = ..................

Acceptance angle, θ= = ...........................

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Result

Numerical aperture of the optic fiber is = …………………

Angle of acceptance = ……………….

Self evaluation

1. What is the working principle behind optical fibers?

(a)Reflection (b) Refraction (c) Total internal reflection (d) Diffraction

2. Total internal reflection occurs only when the angle of incidence is:

(a)Independent of critical angle (b) Equal to critical angle (c) Lower than critical
angle (d) Greater than critical angle
3. The Sine of the angle of incidence divided by the sine of angle of refraction equals optical density is
called?

(a) Newton’s law (b) Snell’s law (c) Pascal’s law (d) Bernoulli’s law
4. Optical fibers are often used in preference to copper wire when transmitting data. Which of the
following is not a reason for the preferred use of optical fibers?

(a)Optical fibers are more durable than copper wires (b )Optical fibers can carry
more information than copper wires (c) fibers are cheaper than copper wires
(d)optical fibers are better conductors of electricity than copper wires.
5. In refraction, when ray goes from air to glass at an angle of incidence, which one of these happens?

(a)The ray is absorbed (b)The angle of incidence is greater than angle of refraction
(c) The angle of incidence is less than the angle of refraction (d) All the ray is
reflected off the surface.
Assignment

1. Define numerical aperture and acceptance angle of an optical fiber.

2. A detector is placed at a distance 2 mm from a laser source emitting red light. Find the numerical
aperture of the plastic-glass fiber used.

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 Hall effect experiment: Determination of charge carrier density

Aim:

1. To determine the Hall voltage developed across the sample material.

2. To calculate the Hall coefficient and the carrier concentration of the sample material.

Apparatus:

Two solenoids, Constant current supply, Four probe, Digital gauss meter, Hall effect apparatus (which
consist of Constant Current Generator (CCG), digital milli voltmeter and Hall probe).

Theory:

If a current carrying conductor placed in a perpendicular magnetic field, a potential difference will
generate in the conductor which is perpendicular to both magnetic field and current. This phenomenon is
called Hall Effect. In solid state physics, Hall effect is an important tool to characterize the materials
especially semiconductors. It directly determines both the sign and density of charge carriers in a given
sample.

Consider a rectangular conductor of thickness t kept in XY plane. An electric field is applied in X-

direction using Constant Current Generator (CCG), so that current I flow through the sample. If w is the
width of the sample and t is the thickness. There for current density is given by

Jx=I/wt (1)

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 Fig.1 Schematic representation of Hall Effect in a conductor.
CCG – Constant Current Generator, JX – current density
ē – electron, B – applied magnetic field
t – thickness, w – width
VH – Hall voltage

If the magnetic field is applied along negative z-axis, the Lorentz force moves the charge carriers (say
electrons) toward the y-direction. This results in accumulation of charge carriers at the top edge of the
sample. This set up a transverse electric field Ey in the sample. This develop a potential difference along
y-axis is known as Hall voltage VH and this effect is called Hall Effect.

A current is made to flow through the sample material and the voltage difference between its top and
bottom is measured using a volt-meter. When the applied magnetic field B=0,the voltage difference will
be zero.
We know that a current flows in response to an applied electric field with its direction as conventional
and it is either due to the flow of holes in the direction of current or the movement of electrons
backward. In both cases, under the application of magnetic field the magnetic Lorentz force,
causes the carriers to curve upwards. Since the charges cannot escape from the material, a
vertical charge imbalance builds up. This charge imbalance produces an electric field which counteracts
with the magnetic force and a steady state is established. The vertical electric field can be measured as a
transverse voltage difference using a voltmeter.
In steady state condition, the magnetic force is balanced by the electric force. Mathematically we can
express it as
(2)

Where 'e' the electric charge, 'E' the hall electric field developed, 'B' the applied magnetic field and 'v' is
the drift velocity of charge carriers.

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And the current 'I' can be expressed as,
(3)
Where 'n' is the number density of electrons in the conductor of length l ,breadth 'w' and thickness 't'.
Using (1) and (2) the Hall voltage V H can be written as,

(4)

by rearranging eq(4) we get

(5)

Where RH is called the Hall coefficient.

RH=1/ne (6)

Procedure:

Controls

Combo box

Select procedure: This is used to select the part of the experiment to perform.

1) Magnetic field Vs Current. 2) Hall effect setup.

Select Material: This slider activate only if Hall Effect setup is selected. And this is used to select the
material for finding Hall coefficient and carrier concentration.

Button

Insert Probe/ Remove Probe: This button used to insert/remove the probe in between the solenoid.
Show Voltage/ Current: This will activate only if Hall Effect setup selected and it used to display the
Hall voltage/ current in the digital meter.
Reset: This button is used to repeat the experiment.

Slider

Current : This slider used to vary the current flowing through the Solenoid.
Hall Current: This slider used to change the hall current

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Thickness: This slider used to change the thickness of the material selected.
Procedure for doing the simulation:

To measure the magnetic field generated in the solenoid

1. Select Magnetic field Vs Current from the procedure combo-box.

2. Click Insert Probe button

3. Placing the probe in between the solenoid by clicking the wooden stand in the simulator.

4. Using Current slider, varying the current through the solenoid and corresponding magnetic field
is to be noted from Gauss meter.

Table(1)

Trial No: Current through solenoid Magnetic field generated

1
2
3
4

Hall Effect apparatus

1. Select Hall Effect Setup from the Select the procedure combo box
2. Click Insert Hall Probe button
3. Placing the probe in between the solenoid by clicking the wooden stand in the simulator.
4. Set "current slider" value to minimum.
5. Select the material from “Select Material” combo-box.
6. Select the Thickness of the material using the slider Thickness.
7. Vary the Hall current using the sllider Hall current.
8. Note down the corresponding Hall voltage by clicking “show voltage” button.
9. Then calculate Hall coefficient and carrier concentration of that material using the equation

RH=VHt/(I*B)
Where RH is the Hall coefficient
RH=1/ne
And n is the carrier concentration

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Repeat the experiment with different magnetic file.

Trial Magnetic Field Thickness (t) Hall current, Hall Voltage

RH
No: (Tesla T) m mA mV
1
2
3
4
5

Procedure for doing real lab

1. Connect ‘Constant current source’ to the solenoids.

2. Four probe is connected to the Gauss meter and placed at the middle of the two solenoids.
3. Switch ON the Gauss meter and Constant current source.
4. Vary the current through the solenoid from 1A to 5A with the interval of 0.5A, and note the
corresponding Gauss meter readings.
5. Switch OFF the Gauss meter and constant current source and turn the knob of constant current
source towards minimum current.
6. Fix the Hall probe on a wooden stand. Connect green wires to Constant Current Generator and
connect red wires to milli voltmeter in the Hall Effect apparatus
7. Replace the Four probe with Hall probe and place the sample material at the middle of the two
solenoids.
8. Switch ON the constant current source and CCG.
9. Carefully increase the current I from CCG and measure the corresponding Hall voltage VH. Repeat
this step for different magnetic field B.
10. Thickness t of the sample is measured using screw gauge.
11. Hence calculate the Hall coefficient RH using the equation 5.
12. Then calculate the carrier concentration n. using equation 6.

Result
Hall coefficient of the material = .........................
Carrier concentration of the material =.......................... m-3

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Self Evaluation

1. The experiment which directly determines both the sign and density of charge carriers in a sample
material is
a) Four probe method b) Hall experiment c) Quincke's method d)None of these
2. If a current carrying conductor placed in a perpendicular magnetic field, a potential difference will
generate in the conductor which is perpendicular to both magnetic field and current. This
phenomenon is called
(a)Peltier effect (b) Joule effect (c) Thomson effect (d) Hall effect
3. The quantity 1/(ne) where 'n' is the number density of charge carriers and 'e' is the electric charge
represents.
(a) Thomson effect (b) Joule effect (c) Hall coefficient (d) Peltier effect
4. Negative Hall coefficient indicates that the charge carriers are.
(a) Holes (b) Electrons (c) Both holes and electrons d) None of the above
5. The Hall coefficient RH for a sample material is independent of.
(a) Number density of charge carriers (b) Temperature (c) Nature of material (d)
Dimensions of material.
Assignment:

1. Define and explain Hall Effect? Derive an expression for Hall Coefficient.
2. Calculate the carrier concentration for a Ge semiconductor of thickness 0.3mm.

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