Physics-investigatory To find the refractive indices of

(a) water (b) oil (transparent) using a plane mirror, an

equiconvex
le n s - G G o o g l e D o c s
Corporate law (H in du st t an I nt er n at ion a l S chool
Guindy)

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Physics

Investigatory Project

Year :- 2023-2024

BY :- Sameer
Chauhan ROLL No. :-
Class :- XII

To find the refractive indices of (a) water (b)

oil

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 To find the refractive indices of (a) water (b)
oil

CERTIFICATE

This is to certify that Master Sameer Chauhan, a student of class XII

has successfully completed the research on the below mentioned
project under the guidance of (Subject
Teacher) during the year 2023-24 in partial fulfilment of Physics
Practical Examination conducted by AISSCE, New Delhi.

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 To find the refractive indices of (a) water (b)
oil

ACKNOWLEDGEMENT

In the accomplishment of this project successfully, many people

have best owned upon me their blessings and the heart
pledged support, this time I am utilizing to thank all the people
who have been concerned with project.

Primarily I would thank god for being able to complete this

project with success. Then I would like to thank my Physics
Teacher , whose valuable guidance has
been the ones that helped me patch this project and make it
full proof success his suggestions and his instructions has
served as the major contributor towards the completion of the
project.

Then I would like to thank my parents and friends who have

helped me with their valuable suggestions and guidance has
been helpful in various phases of the completion of the project.

Last but not the least I would like to thank my classmates who
have helped me a lot.

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 To find the refractive indices of (a) water (b)
oil

INDEX
Sr No. Content Tile Page no.
1. Introduction 4
2. AIM 5
3. Apparatus 5
4 Diagram G
5. Theory 7
G. Procedure 9
7. Observations 12
8. Calculations 14
9. Result 15
10. Precautions 15
11. Sources of Error 1G
12. Bibliography 17

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 To find the refractive indices of (a) water (b)
oil

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

𝑛 =
𝐶
�
�

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.

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 To find the refractive indices of (a) water (b)
oil

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

APPAR ATUS
Convex Lens
Plane Mirror
Wate
r Oil
Clamp Stand
An Optical Needle
Plumb Line
Knitting Needle
Half Meter Scale
Glass Slab
Spherometer
5

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To find the refractive indices of (a) water (b)
oil

DIAGRAMS

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To find the refractive indices of (a) water (b)
oil

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
𝐹𝑓
1 or
2
1

−𝐹
f
+ =
𝑓
𝑓
𝐹 =
1
2
1 𝑓
2

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

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

1 = (𝑛 − 1)𝖫� 1− 1
�1 ⌋
� �
�2 �2

=(𝑛 − 1)𝖫 𝑅
1
− ∞1 ⌋
1

− 0⌋
1
= (n-1)𝖫
�
�
𝑛−1
1
𝑓
2 = �

𝑓 +
𝑅
�

1
n=
2

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To find the refractive indices of (a) water (b)
oil
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To find the refractive indices of (a) water (b)
oil

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
6ℎ 2
R=

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.

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 To find the refractive indices of (a) water (b)
oil

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 metre scale. Also
measure the distance between the tip of the needle and
the 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).

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 To find the refractive indices of (a) water (b)
oil

(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.

10

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To find the refractive indices of (a) water (b)
oil

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 it 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 +𝑙 +𝑙
1 2 3
l= 3

11
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 To find the refractive indices of (a) water (b)
oil

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.No Initial reading No. of Final Additional h=n x Mean

of the C.S. on complete reading of C.S div. pitch “h”
the convex rotations the c.s on moved + m x (cm)
lens the glass L.C
(a) (n) slab

1 62 0 6.5 55.5 0.555 0.5775

2 64 0 4 60 0.6

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 To find the refractive indices of (a) water (b)
oil

To measure focal length ‘f’ of convex lens

Distance of needle tip from

Area S.No Tip of the upper Upper Mean Focal
𝑥 +𝑥
between surface of the surface of Length
1 2
lens and convex lens(cm) the plane x= 2 (cm)
plane mirror X1 mirror(cm)
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

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To find the refractive indices of (a) water (b)
oil

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:

𝑅 =6 + = 2. 8861 𝑐𝑚
2
𝑙 ℎ
2
ℎ

Measurement of refractive indices of water and oil

1) With water between the convex lens and the plane mirror:

µ = 1 + 𝑅
= 1 + 2.8861
= 1. 0831
1 𝑓 34.7
2

2) With oil between the convex lens and the plane Mirror

µ = 1 +
𝑅 = 1 + 2.8861
1 = 1. 2886
0
2
�
�3

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oil

Results

The refractive index of water is µ1 = 1.0831

The refractive index of oil is µ2 = 1.2886

PRECAUTIONS

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.
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 To find the refractive indices of (a) water (b)
oil

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.

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 To find the refractive indices of (a) water (b)
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BIBLIOGRAPHY

● HELP FROM TEACHERS

● NCERT TEXTBOOK
● NCERT Physics Lab Manual
● britannica.com
● www.scribd.com
● microscopyu.com

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