This document is a certificate for a student who completed a physics project on measuring the refractive indices of various liquids. The project was carried out in the school laboratory during the 2014-2015 academic year, as part of the curriculum for the ALL INDIA SENIOR SECONDARY EXAM. The student measured the refractive indices of liquids including water, vinegar, vegetable oil and glycerine using a hollow glass prism. The speeds of light in the liquids were also calculated using the refractive indices and the known speed of light in a vacuum.

1. CERTIFICATE
This is to certify that …………………………...... of Class
XII-A has completed the Physics project titled
“REFRACTIVE INDICES OF VARIOUS LIQUIDS” in
partial fulfilment of curriculum of ALL INDIA SENIOR
SECONDARY EXAM (CBSE). This project was carried out
in the school laboratory of K.V. Pangode during the
academic year 2014-15.
Internal Examiner External Examiner
School Seal Principal
1

2. Acknowledgement
I take this opportunity to express my gratitude in
few words and respect to all those who helped me in the
completion of this project. The successful completion of
any task would be incomplete without mentioning the
names of those persons who helped to make it possible.
It is my humble pleasure to acknowledge my deep
senses of gratitude and heartfelt indebtedness to my
teacher Smt.Lekshmi Devi for her valuable support,
constant help and guidance at each and every stage,
without which this project would not have come forth.
I also register my sense of gratitude to our Principal,
my teacher Shri K. B. K Unnithan, for his immense
encouragement that has made this project successful.
I would also like to thank my friends and family for
their endless support without which I could not have
completed this work in time.
2

3. INDEX
3
Sl no: Title
Page
no:
1. Certificate 02
2. Acknowledgement 03
3. Introduction 05
4. Experiment 13
5. Bibliography 23

4. Introduction
This project envisages the use of hollow glass prism to
calculate the refractive indices of various liquids. The
hollow glass prism is filled with the liquid and then the
deviation in the path of the ray of light, as it suffers
refraction, is studied. Readings of the experiment are
noted with the various liquids and refractive index is
calculated for each pair of media.It has been assumed
that the refractive index of the liquids is with respect to
that of air.Important general terms related to refraction
of light are given below:-
Refraction:
In a homogenous medium, light travels along a straight
line. But whenever it falls on the surface of another
medium, a very small fraction of it is reflected back and
most of the light passes
into the medium, though with a change of direction. This
phenomenon of the bending of light at the surface of
separation of two media is called refraction of light.
4

5. Cause of Refraction:
The phenomenon of refraction takes place when a beam
of light enters a medium in which light travels with a
different velocity.
Laws Of Reflection:
1. The reflected ray, the incident ray, and the normal at
the point of incidence all lie in the same plane.
2. The angle of incidence is equal to the angle of
reflection.
Laws Of Refraction:
1.The incident ray, the refracted ray, and the normal at
the point of incidence all lie in the same plane.
2.For any two given media the ratio sin i / sin r is a
constant (where i is the angle of incidence, r is the angle
of refraction). This is also called Snell's Law.
Refractive Index:
5

6. For a monochromatic light, the ratio of the sine of the
angle of incidence to the angle of refraction is a
constant for two given media in contact.If "i" is the angle
of incidence and "r" the angle of
refraction then sin i / sin r = constant.
6

7. This constant is called the refractive index. For most
purposes it may be assumed that the refractive index is
w.r.t. air. When light travels from rarer to denser medium it
bends
towards the normal and when it travels from denser to
rarer medium it bends away from the normal. It has been
experimentally determined that refractive index of a
substance,
µ= c/v.
c=the speed of light in vacuum
v= the speed of light in the substance
7

8. Prism:
A portion of transparent medium bounded by two
plane surfaces inclined to each other at a suitable angle is
called a prism. The angle between the two faces is known
as the angle of the angle of the prism or the refracting
angle.
Refractive Edge:
The line of interaction of the edges of the planes is known
as the refractive edge of the prism.
Angle of Deviation:
The angle through which the incident ray of light is
deviated is called the angle of deviation. It is the angle
8

9. between the emergent
ray and the incident ray produced.
Angle of Minimum Deviation:
As the value of the angle of incidence (i) increases, the
angle of deviation (d) decreases till for a particular value of
angle of incidence, it attains a minimum value 'Dm' called
the
angle of minimum deviation and then increases again. At
this angle (Dm) the incident ray and the emergent ray are
symmetrical w.r.t. the refracting surfaces.
Critical Angle:
It is that angle of incidence in the denser medium for
which the corresponding angle of refraction in the rarer
medium is 90 degrees.
µ = l/sin c where
µ = Refractive Index
9

10. c= critical angle
Relation between refractive index and critical angle
according to Snell's Law:
b
µa= sin i/ sin r where i = c and r = 90°
b
µa = sin c/ sin 90° = sin c
But b
µa = 1/ a
µb
i.e. 1/ a
µb = sin
c or a
µb= 1/sin
c
PRISM
FORMULA
10

11. Let ABC represent a section of the glass prism and let L be a
ray incident at an angle "I" on the first face AB of the prism
at a point "E". NN’
is the normal to this face.
The material of the prism is denser with respect to air, as
such the ray would refract in the direction EF making an
angle r with the normal, reaching the second face AC of the
prism at the point F making an angle e with the normal MM’
.
The ray emerges in the
direction FS bending away from the normal making an angle
"e" with the normal.
If the incident ray PE be produced forwards to meet FS (also
to be produced backwards) at G then the angle HGF is called
the angle of deviation and is represented by D. Angle "BAC"
is called the refracting angle of the prism and represented by
"A".
11

12. From the figure it can be proved:
D = (I + e) - (r1 + r2) (using exterior angle property of
a triangle)
and A = (r1 + r2)
Therefore A + D = I + e; when angle of deviation D has
the minimum value Dm, the following conditions are
fulfilled
I = e and r1 = r2 = r (say)
Applying these conditions in the equation
A = 2r Or r = A/2 A + Dm = 2I
I = (A + Dm)/2
Since 1
µ2 = sin i/ sin r
1
µ = {sin(A + Dm)/2}/{sin A/2}
12

13. Experiment
AIM:
To find out the refractive indices of different liquids using
a hollow prism and to find the speed of light in given
transparent fluids.
APPARATUS:
 Hollow glass prism
 Drawing board
 Pins
 Meter scale
 Protractor
 Sheets of white paper
 Various liquids
a)Glycerine
b)Water
c) Vinegar
d)Vegetable Oil
THEORY:
Light is an electromagnetic radiation that is visible to the
human eye usually having a wavelength in the range of
400 nm to 700 nm between the infrared, with longer
wavelengths and the ultraviolet with the shorter
wavelength. The speed of light in vacuum is found to be

14. exactly 299,792,458 m/s. Observable events that result
from the interaction of light and matter are called optical
phenomenon. Refraction is a surface phenomenon due to a
change in its transmission medium.
When a ray of light passes from one medium into the other,
it either bends towards the normal or away from the
normal in the second medium. This phenomenon is known
as the refraction of light.
A prism is a transparent optical element with flat, polished
surfaces that refract light. Prisms can be made from any
material that is transparent including glass, plastic and
fluorite. A prism can be used to break light up into its
constituent spectral colors. Prisms can also be used to
reflect light, or to split light into components with different
polarizations.

15. For a particular pair of two media and for a particular
wavelength of light (colour) the ratio of the sine of the
angle of incidence and the sine of the angle of refraction is
a constant quantity called the refractive index of the
second medium w.r.t. the first. It is represented by ----- 2
µ1
= sin i / sin r.The value of the angle of incidence "i" can be
obtained in the terms of the refracting angle "A" of the
prism and the angle of minimum deviation "Dm" and the
angle of refraction "R" can also be obtained in terms of the
refracting angle "A" of the prism. Thus we find that we can
use the above relation derived for determining the
refractive index.
The experiment thus consists in finding the value of the
refracting angle "A" of the prism and the value of the angle
of minimum deviation Dm.
The refractive index of the liquid
Is given by the formula:
µ = {sin(A + Dm)/2}/{sin A/2}
For finding the value of Dm a curve is plotted between

16. angles of incidence (i) and their respective angles of
deviations (d).
PROCEDURE
A) For finding the angle of prism
 Take a piece of white paper, fix it on a drawing board
using board pins.
 Place the hollow glass prism on the sheet and carefully
draw its outline. Draw a normal and carefully draw its
outline.
 Draw a normal and an incident ray at an angle of 35
degrees with the normal on side AB of the prism.
 Fix two pins P1 and P2 on the incident ray which are at
least 5 cm apart.
 Fill the prism with water and place it over its outline.
Observe the refracted ray that comes after refraction
from the face AB
of the prism.
 Fix two more pins P3 and P4 to cover the image of P1 and
P2.
 Obtained angles r1 and r2 and add them to obtain the
angle of the prism.
B) For finding the angle of minimum deviation
 Fix a white sheet of paper on a drawing board using
board pins

17.  Place a hollow glass prism on the sheet and carefully
draw its outline. Draw a normal and an incident ray of
angle of incidence 35 degrees on the side AB of the
prism.
 Fix two pins P1 and P2 on the incident ray at least 5 cm
apart.
 Fill the hollow prism with water and place it over its
drawn outline. Observe the refracted ray which comes
after
refraction by placing two more pins P3 and P4 covering P1
and P2.
 Extended the incident and refracted ray to obtain the
angle of deviation, D.
 Repeat the above procedure taking other liquids and the
angles of incidence as 40° , 45° , 50° , 55° and 60°.
Note the lowest obtained value of angle of deviation as
the angle of minimum deviation, Dm .
 Using the value of the angle of prism (A) and the angle
of minimum deviation (Dm), calculate the value of the
refractive index of the liquids by using the equation
given in the theory.
 Select suitable scales to represent the angle of
incidence along the X-axis and angle of deviation along

18. the Y-axis and plot a graph. The graph gives the value of
Dm, which is the minimum most point of the parabola.
S.No.
Name of Liquid
Angle of
Incidence
Angle of
Deviation
1 35° 25°
2 40° 24°
3 Water 45° 23°
4 50° 25°
5 55° 27°
6 60° 28°
7 35° 26°
8 40° 25°
9 Vinegar 45° 23.5°
10 50° 25°
11 55° 27°
12 60° 28°
13 30° 49°
14 35° 40°
15 Vegetable Oil 40° 39°
16 45° 34°
17 50° 36°
18 55° 39°
19 35° 41°
20 40° 38°
21 Glycerine 45° 36°
22 50° 35°
23 55° 36°
24 60° 38°
OBSERVATIONS:

19. CALCULATIONS:
A) Refractive index of liquids
Angle of prism (A) = 60°
Formula used: µ= {sin ((A + Dm)/2}/{sin (A/2)}
Water:
Dm=23°
Therefore µ =
sin 41.5
sin 30
=
0.6626
0.5
=1.3252
Vinegar:
Dm=23.5°
Therefore µ =
sin 41.25
sin 30
=
0.6593
0.5
=1.
3186
Vegetable Oil:
Dm=34°
Therefore µ =
sin 47.0
sin 30
=
0.7314
0.5
=1.4628
Glycerine:

20. Dm=35°
Therefore µ =
sin 47.5
sin 30
=
0.7373
0.5
=1.4746
Sl
no
Liquid
Speed of light v=
c
n (m/s)
Speed of
light
(m/s)
1 Water 3×108
/1.3252 2.26×108
2 Vinegar 3×108
/1.3186 2.27×108
3 Vegetable oil 3×108
/1.4626 2.05×108
4 Glycerine 3×108
/1.4726 2.03×108
B) Speed of light in liquids
Graph for angle of minimum deviation

21. RESULT
The refractive indexes of the four liquids were found to
be as follows:-
 Water, µ = 1.3252
 Vinegar, µ = 1.3186
 Vegetable Oil, µ = 1.4628
 Glycerine, µ = 1.4726
The speeds of light in the four liquids were found to be
as follows:-
 Water, v=2.26×108
m/s
 Vinegar, v=2.27×108
m/s
 Vegetable oil, v=2.05×108
m/s
 Glycerine, v=2.03×108
m/s
PRECAUTIONS

22.  The position of the prism should not be disturbed
on the white sheet.
 There should be no parallax between the pins P1,
P2 and their images P3, P4.
 The angles should be measured carefully.
 The curve of the graph should be smooth.
SOURCES OF ERROR
 Pin pricks may be thick
 Measurement of angles may be wrong

23. BIBLIOGRAPHY
Physics Class XII NCERT Textbook
Comprehensive Practical Physics by Lakshmi
Publications
www.hyperphysics.com
Google images