St. Anthony’s sr.

Secondary school
Udaipur (raj.)

Session :- 2024-25

Supervised by : Mrs. Seema kamra, Physics

St. Anthony’s school udaipur

Submitted by : Dhwani lohar

Class:- xII sci
Subject:- physics
St. Anthony’s school udaipur
 Acknowledgement
In the accomplishment of this project
successfully many people have best owned
upon me as their blessing and the heart
pledged support, this time I am utilizing to
thank all the people who have been concerned
with project.
Primarily I would like to thank god for being
able to complete this project with success. Then
I would like to thank my Physics teacher Mr.
Mrs. Seema
Mukesh kamra
k. Bagdi Sir whose valuable guidance
has been the ones that helped me patch this
project and make it full proof success his
suggestions and instructions has served as the
major contribution. Then I would like to
thanks my Parents and Friends who have
helped me with their valuable suggestions and
guidance have been helpful in the various
phases of the completion of this project. Last I
would like to thank Myself for my
determination and hard work required for the
completion in this project.
 Certificate
This is to certify that Dhwani Lohar,
This is to certify that Shalu singh, a
a student of class 12th science has
student of class XII-B has successfully
successfully
completed the completed
research the
onresearch
Study on
of
different
the studytypes ofinternal
of total transformers the
reflection
under the guidance of Mr. Mukesh
under the guidance of Mrs. Seema
kumar Bagdi (Subject Teacher) during
Kamra,
the subject teacher
year 2019-20 during
in partial the
fulfilment
ofyear
Physics practical
2024-25 in partial examination
fulfilment of
conducted CBSE Board.
physics, practical examination
conducted CBSE board
Signature of the external examiner
Signature of the Physics teacher

Content
 Introduction
 Optical description
 Critical angle
 Phase shift upon total
internal reflection
 Total internal reflection
in diamond
 Applications of total
internal reflection
 Examples in everyday
life
 Total Internal
Reflection using a Soda
Bottle{EXPERIMENT}
 Bibliography
 INTRODUCTION
Total internal reflection is an optical phenomenon that
happens when a ray of light strikes a medium boundary
at an angle larger than a particular critical angle with
respect to the normal to the surface. If the refractive index
is lower on the other side of the boundary and the incident
angle is greater than the critical angle, no light can pass
through and all of the light is reflected. The critical angle
is the angle of incidence above which the total internal
reflectance occurs.
When a light beam crosses a boundary between materials
with different kinds of refractive indices, the light beam
will be partially refracted at the boundary surface, and
partially reflected. However, if the angle of incidence is
greater (i.e. the ray is closer to being parallel to the
boundary) than the critical angle – the angle of incidence
at which light is refracted such that it travels along the
boundary – then the light will stop crossing the boundary
altogether and instead be totally reflected back internally.
This can only occur where light travels from a medium
with a higher [n1=higher refractive index] to one with a
lower refractive index [n2=lower refractive index]. For
 example, it will occur when passing from glass to air, but
not when passing from air to glass.

OPTICAL DISCRIPTION
Total internal reflection can be demonstrated using a semi-
circular block of glass or plastic. A "ray box" shines a narrow
beam of light (a "ray") onto the glass. The semi-circular shape
ensures that a ray pointing towards the centre of the flat face
will hit the curved surface at a right angle; this will prevent
refraction at the air/glass boundary of the curved surface. At
the glass/air boundary of the flat surface, what happens will
depend on the angle? Where is θC the critical angle
measurement which is caused by the sun or a light source
(measured normal to the surface):
• If θ < θC, the ray will split. Some of the ray will reflect
off the boundary, and some will refract as it passes through.
This is not total internal reflection.
• If θ > θC, the entire ray reflects from the boundary. None
passes through. This is called total internal reflection.
This physical property makes optical fibres useful and
prismatic binoculars possible. It is also what gives diamonds
their distinctive sparkle, as diamond has an unusually high
refractive index.
 CRITICAL ANGLE
The critical angle is the angle of incidence above which
total internal reflection occurs. The angle of incidence is
measured with respect to the normal at the refractive
boundary (see diagram illustrating Snell's law). Consider
a light ray passing from glass into air. The light
emanating from the interface is bent towards the glass.
When the incident angle is increased sufficiently, the
transmitted angle (in air) reaches 90 degrees. It is at this
point no light is transmitted into air. The critical angle is
given by Snell's law.
𝒏𝟏 𝐬𝐢𝐧 𝜽𝒊 = 𝒏𝟐 𝐬𝐢𝐧 𝜽𝒕

Rearranging Snell's Law, we get incidence

𝒏𝟐
𝐬𝐢𝐧 𝜽𝒊 = 𝐬𝐢𝐧 𝜽𝒕
𝒏𝟏

To find the critical angle, we find the value for 𝜽𝒊

when 𝜽𝒕 = 𝟗𝟎° and thus 𝐬𝐢𝐧 𝜽𝒕 = 𝟏 .The resulting
value of is equal to the critical angle 𝜽𝒄 .
Now, we can solve for 𝜽𝒊 , and we get the equation for the
critical angle:
𝒏𝟐
𝜽𝒄 = 𝜽𝒊 = 𝐬𝐢𝐧 𝟏
𝒏𝟏
If the incident ray is precisely at the critical angle, the
refracted ray is tangent to the boundary at the point of
incidence. If for example, visible light were travelling
through acrylic glass (with an index of refraction of
1.50) into air (with an index of refraction of 1.00), the
calculation would give the critical angle for light from
acrylic into air, which is

𝟏
𝟏. 𝟎𝟎
𝜽𝒄 = 𝐬𝐢𝐧 = 𝟒𝟏. 𝟖
𝟏. 𝟓𝟎
PHASE SHIFT UPON
TOTAL INTERNAL
REFLECTION
A lesser-known aspect of total internal reflection is that
the reflected light has an angle dependent phase shift
between the reflected and incident light. Mathematically
this means that the Fresnel reflection coefficient becomes a
complex rather than a real number. This phase shift is
polarization dependent and grows as the incidence angle
deviates further from the critical angle toward grazing
incidence.
The polarization dependent phase shift is long known and
was used by Fresnel to design the Fresnel rhomb which
allows transforming circular polarization to linear
polarization and vice versa for a wide range of
wavelengths (colours), in contrast to the quarter wave
plate. The polarization dependent phase shift is also the
reason why TE and TM guided modes have different
dispersion relations.
 REFLECTION IN
DIAMOND
From glass to air the critical angle is about 42o but it varies
from one medium to another. The material that gives the
smallest critical angle is diamond. That is why they sparkle so
much! Rays of light can easily be made to 'bounce around
inside them' by careful cutting of the stone and the refraction at
the surfaces splits the light into a spectrum of colours!
Relatively speaking, the critical angle 24.4o for the diamond-
air boundary is extremely small. This property of the
diamond-air boundary plays an important role in the brilliance
of a diamond gemstone. Having a small critical angle, light
has the tendency to become "trapped" inside of a diamond once
it enters. Most rays approach the diamond at angles of
incidence greater than the critical angle (as it is so small) so a
light ray will typically undergo TIR several times before
finally refracting out of the diamond. This gives diamond a
tendency to sparkle. The effect can be enhanced by the cutting of
a diamond gemstone with a 'strategically' planned shape.
 APPLICATIONS OF
TOTAL INTERNAL
REFLECTION
 Total internal reflection is the operating principle of
optical fibres, which are used in endoscopes and
telecommunications.
 Total internal reflection is the operating principle of
automotive rain sensors, which control automatic
windscreen/windshield wipers.
 Another application of total internal reflection is the
spatial filtering of light.
 Prismatic binoculars use the principle of total internal
reflections to get a very clear image.
 Gonioscopy employs total internal reflection to view the
anatomical angle formed between the eye's cornea and iris.
 Optical fingerprinting devices use frustrated total internal
reflection in order to record an image of a person's
fingerprint without the use of ink.
 A Total internal reflection fluorescence microscope uses the
evanescent wave produced by TIR to excite fluorophores
close to a surface. This is useful for the study of surface
properties of biological samples.
 EXAMPLES IN
EVERYDAY LIFE
Total internal reflection can be observed while swimming, when
one opens one's eyes just under the water's surface. If the water
is calm, its surface appears mirror-like.
One can demonstrate total internal reflection by filling a sink or
bath with water, taking a glass tumbler, and placing it upside-
down over the plug hole (with the tumbler completely filled
with water). While water remains both in the upturned tumbler
and in the sink surrounding it, the plug hole and plug are
visible since the angle of refraction between glass and water is
not greater than the critical angle. If the drain is opened and
the tumbler is kept in position over the hole, the water in the
tumbler drains out leaving the glass filled with air, and this
then acts as the plug. Viewing this from above, the tumbler now
appears mirrored because light reflects off the air/glass
interface.
This is different phenomenon from reflection and refraction.
Reflection occurs when light goes back in same medium.
Refraction occurs when light travels from different mediums.
Here both are not happening. This is due to both and a mixture
of both.Another common example of total internal reflection is
a critically cut diamond. This is what gives it maximum spark.
 TOTAL INTERNAL
REFLECTION USING
A SODA BOTTEL
Explanation
In this case, nair = 1.00 nwater = 1.33. Therefore:

In this demo light will continually reflect through the stream of

water creating total internal reflection (TIR). The stream of
water will 'carry' the light though, to the end of the stream.
 Total Internal Reflection is the principle
behind fiber optics.

Materials
 empty soda pop bottle (2 liter)
 tape
 hand drill
 drill bits
 water
 green laser
 bucket
old books, etc for stands
Procedure

 First set up the soda bottle by drilling a hole near the

bottom of the bottle. Begin with a drill bit that has a
diameter which is slightly larger than the diameter of the
laser that will be used. We used a 1/4 inch drill bit,
however sizes as small as 7/32 inch worked as well.
 First tape the hole and then fill the bottle with water. The
cap will prevent leaking because it creates a vacuum in the
bottle.
 Stand the soda bottle on top of a stack of books so the hole
is facing the bucket. The laser should be placed in a binder
clip so it stays on, and then set on a stack of books and
papers. The laser should be lined up so that the laser light
goes through the soda bottle, and into the center of the hole.
See for details.
 Carefully remove the tape and then unscrew the top of the
soda bottle. The light should reflect within the stream of
water so that you could see at least a few points of
reflection. The light should be visible through the entire
stream.
  If the reflections of the light aren’t clear, it may be
necessary to expand the hole by drilling through the
existing hole with a larger drill bit. This process may need
to be repeated several times.

Notes
 This is an messy experiment. Be ready to adjust the
bucket which catches the stream of water.
 Also be aware that the stream's curvature will change as
the water level decreases. It will bend closer to the bottle,
and the bucket may need to be adjusted again. When the
water level is a little above the hole there will be no total
internal reflection although the stream will continue. Place
the cap back on, or put the bottle inside of the bucket.
 Make sure to have lots of paper towels! Towels or rags
could be useful too. However, this mess is water, and
therefore easy to clean up.
 Some resources suggest putting a drop of food coloring in
the bottom of the bucket to match the laser light, giving the
appearance that the water has permanently 'trapped' the
colored light.
 BIBLIOGRAPHY
Following Books and websites were a source for my project.

 Wikipedia
 NCERT Physics Textbook for class 12
 Feynman Lectures on Physics
 Google