HEM SHEELA
MODEL SCHOOL
PHYSICS INVESTIGATORY
PROJECT
To find the refractive index of (a) water (b)oil
using a plane mirror and an equiconvex lens and
an adjustable object needle
NAME :
CLASS : XII
ROLL NO. :
SESSION : 2023 - 2024
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Acknowledgement
I would like to express my immense gratitude to
my physics teacher AMIT MUKHARJEE for the help
and guidance she provided for completing this
project.
I also thank my parents who gave their ideas and
inputs in making this project. Most of all I thank
our school management, for providing us the
facilities and opportunity to do this project.
Lastly, I would like to thanks my classmates who
have done this project along with me. Their
support made this project fruitful.
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INDEX
Content Page no.
Acknowledgement 01
Introduction 03
Objective/Aim 04
Materials Required 04
Theory 5-6
Procedure 7-8
Diagram 19
Observation 10-11
Calculation 12
Result and Precaution 13
Sources of Error 14
Bibliography 15
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OBJECTIVE
To find the refractive index of water, oil
using a plane mirror and an equiconvex lens
and an adjustable object needle
Materials Required
➢ Convex lens
➢ Plane mirror
➢ Water
➢ Oil
➢ Clamp stand
➢ An optical needle
➢ Plumb line
➢ Knitting needle
➢ Half meter scales
➢ Glass slab
➢ Spherometer
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THEORY
If f1 and f2 be the focal length of glass convex lens and liquid
lens and F be the focal length of their combination then,
𝟏 𝟏 𝟏 𝒇𝒇𝟐
= + or f2 =
𝒇 𝒇𝟏 𝒇𝟐 𝒇𝟏 −𝒇
Liquid lens formed is a planoconcave lens with
𝑅1 = R (radius of curvature of convex lens surface)
𝑅2 = ∞
𝟏 𝟏 𝟏
= (n-1) [ − ]
𝒇𝟐 𝑹𝟏 𝑹𝟐
𝟏 𝟏
= (n-1) [ − ]
𝑹𝟏 ∞
𝟏
= (n-1) [ − 𝟎]
𝑹
𝟏 𝒏−𝟏
=
𝒇𝟐 𝑹
𝑹
n= +1
𝒇𝟐
Where,
n = Refractive index of the liquid
R= The radius of curvature of the convex lens
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The radius of the lower surface of the convex lens is given
by:
𝒍𝟐 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
Fig: Focal length of glass convex lens and liquid lens combination
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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 (fi).
(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)
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(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.
𝒍𝟏 + 𝒍𝟐 + 𝒍𝟑
𝒍=
𝟑
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OBSERVATION
• Pitch of the spherometer = 1 cm
• Least count of the spherometer = 0.01 cm
• Distance between the Legs:
(1). AB = 3cm
(2). BC = 3cm
(3). CA = 3cm
Table for calculation of ‘h’
SLNO: Initial NO. of Final Additional H=n× Mean
reading of complete reading C.S. div pitch+ m “h”
the C.S. on rotations(n) of the moved × L.C. (cm)
the convex C.S. on
lens(a) the slab
1 62 0 6.5 55.5 0.555 0.5775
2 64 0 4 60 0.6
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To measure the focal length ‘f’ of a convex lens
Area Distance of needle tip Mean Focal
between from X= length
SL.
lens and NO: Tip of the Upper x1+x2 (cm)
plane upper surface of 2
mirror surface of the plane
the mirror(cm)
convex X2
lens(cm)
X1
1 30.5 31 30.72 f1= 33.85
Without
liquid
2 36.7 37.2 36.95
1 31.4 31.8 31.6 f2 = 34.7
With water
2 37.5 38.1 37.8
With 1 9.4 9.6 9.5 f3 = 10
oil
2 10.4 10.6 10.5
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s
CALCULATION
Mean Distance Between two legs l = (AB + BC + CA)/3 = 3cm
Mean of h = (0.555 + 0.6)/3 = 0.5775cm
𝒍𝟐 𝒉
To find the radius of curvature of the convex lens R = +
𝟔𝒉 𝟐
= 2.8861cm
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 + f3 = 1 + 10 = 1.2886
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RESULT
➢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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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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BIBLIOGRAPHY
1. NCERT Textbook
2. NCERT Physics Lab Manual
3. www.google.com
4. www.wikipedia.com
5. www.youtube.com
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