Jawahar Navodaya Vidyalaya,

Idukki

PHYSICS INVESTIGATORY
PROJECT

TOPIC: THE REFRACTIVE INDICES OF (a)WATER,

(b)OIL (TRANSPARENT) USING A PLANE MIRROR,
AN EQUICONVEX LENS, AND AN ADJUSTABLE
OBJECT NEEDLE”

Submitted by: Rishikrishna KS

Class: XII A
 Roll No: 31

CERTIFICATE
This is to certify that Rishikrishna=KS of class XII A
has successfully completed his physics investigatory
project work on the topic “TO FIND THE REFRACTIVE
INDEX OF (A)WATER, (B)OIL (TRANSPARENT) USING A PLANE
MIRROR, AN EQUICONVEX LENS, (MADE FROM A GLASS OF
KNOWN REFRACTIVE INDEX) AND AN ADJUSTABLE OBJECT
NEEDLE”, under the supervision and guidance of Mr.
Saji PC (PGT Physics).

Sign of internal
examiner:

Sign of external
examiner:

ACKNOWLEDGEMENT
I would like to express my immense gratitude to my physics
teacher Mr. Saji PC sir for the help and guidance he provided
for completing this project
I also thank my parents for giving their ideas and inputs in
making this project. Most of all I thank my school management,
for providing us the facilities and opportunity to do this project.
Lastly, I would like to thank my group members who helped me
throughout this project and made this experience fruitful

-Rishikrishna KS
 INTRODUCTION
In optics, the refractive index or index of refraction n of
a material is a dimensionless number that describes
how light propagates through that medium. It is defined as

C
n=
V

Where c is the speed of light in vacuum and v is the phase

velocity of light in the medium. For example, the refractive
index of water is 1.333; meaning that light travels 1.333
times faster in a vacuum than it does in water.

REFRACTION OF A LIGHT RAY

 AIM
To find the refractive indexes of (a) water
(b) oil using a plane mirror, an equiconvex lens, and
an adjustable object needle.

APPARATUS
 Convex Lens
 Plane Mirror
 Water
 Oil
 Clamp Stand
 An Optical Needle
 Plumb Line
 Knitting Needle
 Half Meter Scale
 Glass Slab
 Spherometer
DIAGRAM
 THEORY
1. If f1 and f2 be the focal length of the glass convex lens
and liquid lens and f be the focal length of their
combination then: -

1 1+ 1 Ff2
F =f 1 f 2 or f2 = f −F
1

2. Liquid lens formed a Plano-concave Lens with R1=R

and R2=∞ then by using lens make’s formula

1 1 1
=( n−1 ) ⌊ − ⌋
f2 R 1 R2

1 1
=( n−1 ) ⌊ R 1 − ∞ ⌋

1
= (n-1) ⌊ R −0 ⌋

1
f2
= n−1
R
 R
n =f 2
+1

Where n = Refractive index of the liquid

R = the radius of the curvature of the convex lens.

3. The radius of the lower surface of the convex lens is

given by:
2
l h
R= +
6h 2

Here, l is the average distance between the legs of the

spherometer and h is the difference in the reading of the
spherometer when placed first on the convex lens and
then on plane mirror.

PROCEDURE
(a)For focal length of convex lens:
1. Find the rough focal length of the convex lens.

2. Place a plane mirror on the horizontal base of the iron

stand and then a convex lens on the plane mirror.

3. Hold the needle in the clamp stand and adjust its

position on the stand such that there is no parallax
between tip of the needle and its image.

4. Measure distance between tip and upper surface of the

lens by using a plumb line and half meter scale. Also
measure the distance between tip of needle and upper
surface of the mirror. Take the mean of the two readings.
This means distance will be equal to the focal length of
the convex lens (f1).

(b)For focal length of the combination.

5. Put a few drops of the water on the plane mirror and
put the convex lens over it with its same face above as
before. The water spreads in a form of layer and acts like
a Plano-concave lens.
6. Repeat the steps 3 and 4 to determine the equivalent
focal length of the combination.
7. Record the observation.
8. Repeat the steps 5, 6, 7 for other transparent liquid
(oil).

(c)For radius of curvature of convex lens surface:

9. Determine the pitch and the least count of the

spherometer.

10. Remove the convex lens and dry it completely. Put the
spherometer on this lens surface.
11. All the three legs of the spherometer should be placed
symmetrically on the lens and adjust the central screw tip
to touch the surface of the lens.

12. Remove the spherometer from the surface of the lens

and place on the plane mirror surface and record the
reading.

13. Repeat the steps 10 and 11 three times.

14. Obtain the impressions of the three legs of the

spherometer on a paper and mark them and their average
distance.

l 1+l 2 +l 3
l= 3

OBSERVATIONS
Pitch of the spherometer= 1 cm
Least count of the spherometer = 0.01 cm
Distance between the legs:
(1) AB = 3 cm
(2) BC = 3 cm
(3) CA = 3 cm
Table for calculation of ‘h’

S.N Initial No. of Final Additiona h=n x Mean

o reading of complete reading l C.S div. pitch “h”
the C.S. on rotations of the c.s moved +mx
(cm)
the convex on the L.C
lens glass slab
(n)
(a)
1 62 0 6.5 55.5 0.55 0.5775
5
2 64 0 4 60 0.6
 To measure focal length ‘f’ of convex lens

Distance of needle tip from

Area S.No Tip of the upper Upper Mean Focal

between surface of the surface of x1 + x 2
x= Length
lens and convex lens(cm) the plane 2
plane mirror(cm) (cm)
X1
mirror
X2
Without 1 30.5 31 30.75 f1=
liquid 33.85
2 36.7 37.2 36.95

With water 1 31.4 31.8 31.6 f2=34.

7
2 37.5 38.1 37.8
With oil 1 9.4 9.6 9.5 f3=10
2 10.4 10.6 10.5

CALCULATIONS
Mean distance between two legs
l=
AB+ BC+ CA
3
= 3 cm

( 0.555+0.6 )
Mean of h = 2 = 0.5775 cm

To find the radius of curvature of the convex lens:

2
l h
R= + =2.8861 cm
6h 2

Measurement of refractive indices of water and oil

1)With water between the convex lens and the plane

mirror:

R 2.8861
μ1=1+ =1+ =1.0831
f2 34.7

2) With oil between the convex lens and the plane

 Mirror

R 2.8861
μ2=1+ =1+ =1.2886
f3 10

RESULTS

The refractive index of water is µ1 = 1.0831

 The refractive index of oil is µ2 = 1.2886

PRECATIONS
1. The plane mirror should be clean and fully shining
surface.
2. The liquid taken should be transparent.
3. The parallax should be removed tip to tip.
4. The eye should be at a distance about 30 cm from the
needle while removing the parallax.
5. Only few drops of liquid should be taken so that its layer
should be thick.
6. The legs of the spherometer should be vertical.
7. The centre leg of the spherometer should turn in one
direction only.

SOURCES OF ERROR

1. Liquid may not be quite transparent.

2. The parallax may not be fully removed.
3. The spherometer legs should be placed symmetrical on
the surface of the convex lens.
4. The tip of the central screw should not just touch the
surface of lens or mirror.

BIBLIOGRAPHY

www.wikipedia.com
www.khanacademy.org
https://www.youtube.com/watch?
v=zlGzYqe_OPw&list=PLjyfEeObqzucIyAsnP32Xt
nkgFWHXN57s
https://www.youtube.com/watch?
v=ArVsBLCOjOc