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Goruav

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lOMoARcPSD|58579491

Physics-investigatory To find the refractive indices of (a)


water (b) oil (transparent) using a plane mirror, an equiconvex
lens - Google Docs
Corporate law (Hindustan International School Guindy)

Scan to open on Studocu

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lOMoARcPSD|58579491

‭Physics‬

‭Investigatory Project‬


I CS
YS
‭PH

‭Year :- 2023-2024‬

‭ Y :- Gourav Krishn
B SameerBhardwaj
Chauhan‬
‭ROLL No. :-‬11
‭Class :- XII‬

T‭ o find the refractive indices of (a) water (b)‬


‭oil‬

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lOMoARcPSD|58579491

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

‭CERTIFICATE‬
Gourav Krishn
‭This‬ ‭is‬ ‭to‬ ‭certify‬ ‭that‬ ‭Master‬ ‭Sameer‬
Bhardwaj‭Chauhan‬‭,‬‭a‬‭student‬‭of‬‭class‬‭XII‬


‭has‬ ‭successfully‬ ‭completed‬ ‭the‬ ‭research‬ ‭on‬ ‭the‬ ‭below‬ ‭mentioned‬ CS
‭project‬‭under‬‭the‬‭guidance‬‭of‬‭__________________‬‭(Subject‬‭Teacher)‬
‭during‬ ‭the‬ ‭year‬ 2025-26
‭2023-24‬ ‭in‬ ‭partial‬ ‭fulfilment‬ ‭of‬ ‭Physics‬ ‭Practical‬
I
YS
‭Examination conducted by AISSCE, New Delhi.‬
‭PH

‭1‬

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lOMoARcPSD|58579491

‭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.‬

‭ rimarily I would thank god for being able to complete this‬


P


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

T‭ hen 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.‬

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

‭2‬

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lOMoARcPSD|58579491

‭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 ‭6‬


‭5.‬ ‭Theory‬
CS ‭7‬
‭6.‬ ‭Procedure‬ ‭9‬
I
YS

‭7.‬ ‭Observations‬ ‭12‬


‭PH

‭8.‬ ‭Calculations‬ ‭14‬


‭9.‬ ‭Result‬ ‭15‬
‭10.‬ ‭Precautions‬ ‭15‬
‭11.‬ ‭Sources of Error‬ ‭16‬
‭12.‬ ‭Bibliography‬ ‭17‬

‭3‬

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lOMoARcPSD|58579491

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

‭INTRODUCTION‬

I‭n ‬‭optics‬‭, the refractive index or index of refraction ‭n‬ ‬‭of‬‭a ‬‭material‬‭is a ‭d‬ imensionless‬
‭number‬‭that describes how ‭l‬ight‬‭propagates through‬‭that medium. It is defined as‬
‭𝐶‬
‭𝑛‬ = ‭ ‬
𝑉

W‭ here ‬‭c‬‭is the ‬‭speed of light‬‭in ‬‭vacuum‬‭and ‬‭v‭‬is the ‭p‬ hase‬‭velocity‬‭of 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.‬


I CS
YS
‭PH

‭4‬

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lOMoARcPSD|58579491

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

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

‭APPARATUS‬

I CS
YS


‭ ‬‭Convex Lens‬
‭PH

‭✔‬‭Plane Mirror‬
‭✔‬‭Water‬
‭✔‬‭Oil‬
‭✔‬‭Clamp Stand‬
‭✔‬‭An Optical Needle‬
‭✔‬‭Plumb Line‬
‭✔‬‭Knitting Needle‬
‭✔‬‭Half Meter Scale‬
‭✔‬‭Glass Slab‬
‭✔‬‭Spherometer‬
‭5‬

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lOMoARcPSD|58579491

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

‭DIAGRAMS‬


I CS
YS
‭PH

‭6‬

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lOMoARcPSD|58579491

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

‭THEORY‬
1‭ ‭.‬‬‭If‬‭f‭1‬ ‬ ‭and‬‭f‭2‬ ‬ ‭be the focal length of the glass‬‭convex‬
‭lens and liquid lens and f be the focal length of their‬
‭combination then:-‬

‭𝐹‬‭𝑓‭2‬ ‬
‭‬
1
‭𝐹‬
‭‬
1
‭ ‬‭𝑓‬
= +
‭‬
1
‭𝑓‬‭2‬
‭or f‬‭2‬‭=‬‭𝑓‬ −‭𝐹‬
‭1‬ ‭1‬


2‭ . Liquid lens formed a Plano-concave Lens with‬‭R1=R‬ CS
‭and‬‭R2=∞‬‭then by using lens make’s formula‬
I
YS

‭‬
1 ‭1‬ ‭‬
1
= (‭𝑛‬ − ‭1)‭
‬ ⌊‬ ‭𝑅‬ − ‭⌋‬
‭PH

‭𝑓‬‭2‬ ‭1‬
‭𝑅‬‭2‬

‭1‬ ‭‬
1
‭=‬(‭𝑛‬ − ‭1)‭
‬ ⌊‬ ‭𝑅‬‭1‬ − ∞
‭⌋‬

‭1‬
‭= (n-1)‬‭⌊‬ ‭𝑅‬ − ‭0⌋‬

‭𝑛−
‬ ‭1‬
‭‬
1
‭𝑓‭2‬ ‬
‭=‬
‭‬

‭𝑅‬

‭ ‬
𝑅
‭n =‬‭‬ ‭𝑓‬ + ‭1‬
‭2‬

‭7‬

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lOMoARcPSD|58579491

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

‭Where‬‭n‬‭=‬‭Refractive index of the liquid‬


‭R‬‭=‬‭the radius of the curvature of the convex‬‭lens.‬

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


‭given by:‬
‭2‬
𝑙‭ ‬ ‭‬

‭R =‬‭‬ ‭6‬‭ℎ‬ + ‭2‬


CS
‭ ere,‬‭l‬‭is the average distance between the legs of‬‭the‬
H
I
YS
‭spherometer and‬‭h‬‭is the difference in the reading‬‭of the‬
‭spherometer when placed first on the convex lens and‬
‭PH

‭then on plane‬‭mirror.‬

‭8‬

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lOMoARcPSD|58579491

‭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.‬
I CS
YS
3‭ . Hold the needle in the clamp stand and adjust its‬
‭position on the stand such that there is no parallax‬
‭PH

‭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).‬

‭9‬

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lOMoARcPSD|58579491

‭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.‬ CS
‭7. Record the observation.‬
I
YS
8‭ . Repeat the steps 5, 6, 7 for other transparent liquid‬
‭(oil).‬
‭PH

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

9‭ . Determine the pitch and the least count of the‬


‭spherometer.‬

1‭ 0. Remove the convex lens and dry it completely. Put‬


‭the spherometer on this lens surface.‬

‭10‬

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lOMoARcPSD|58579491

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

1‭ 1. 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.‬

1‭ 2. 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.‬


1‭ 4. Obtain the impressions of the three legs of the‬ CS
‭spherometer on a paper and mark them and their‬
I
‭average distance.‬
YS
‭PH

‭𝑙‭1‬ ‬+‭‬‭𝑙‭2‬ +‭‭𝑙‬ ‬‭3‬


‭l =‬ ‭3‬

‭11‬

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lOMoARcPSD|58579491

‭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 =‬ ‭ cm‬
3


‭(2)‬‭BC
‭(3)‬‭CA
=‬
=‬
‭3 cm‬
‭3 cm‬
I CS
YS
‭PH

‭Table for calculation of ‘h’‬

‭S.No‬ I‭nitial reading‬ N ‭ o.‬ ‭of‬ F‭ inal‬ ‭ dditional‬


A ‭ =n‬‭x‬ M
h ‭ ean‬
‭of the C.S. on‬ ‭complete‬ ‭reading‬ ‭of‬ ‭C.S‬ ‭div.‬ ‭pitch‬ ‭“h”‬
‭the convex‬ ‭rotations‬ ‭the‬ ‭c.s‬ ‭on‬ ‭moved‬ ‭+‬‭m‬‭x‬ ‭(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

‭12‬

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lOMoARcPSD|58579491

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

‭To measure focal length ‘f’ of convex lens‬

‭ istance of needle tip from‬


D
‭Area‬ ‭S.No‬ ‭Tip of the upper‬ ‭Upper‬ ‭Mean‬ F‭ ocal‬
‭between‬ ‭surface of the‬ ‭surface of‬ ‭‭𝑥
‬ ‬‭1+‭‬‭𝑥‬‭2‬ ‭Length‬
‭x=‬ ‬

‭lens and‬ ‭convex lens(cm)‬ ‭the plane‬ ‭2‬ ‭(cm)‬


‭plane mirror‬ ‭X‬‭1‬ ‭mirror(cm)‬
‭X‬‭2‬
‭Without‬ ‭‬
1 ‭30.5‬ ‭31‬ ‭30.75‬ f‭ ‬‭1‬‭=‬
‭liquid‬ ‭33.85‬
‭2‬ ‭36.7‬ ‭37.2‬ ‭36.95‬


‭With water‬ ‭1‬ ‭31.4‬ CS
‭31.8‬ ‭31.6‬ ‭f‬‭2‬‭=34.7‬
‭2‬ ‭37.5‬ ‭38.1‬ ‭37.8‬
I
YS
‭With oil‬ ‭1‬ ‭9.4‬ ‭9.6‬ ‭9.5‬ ‭f‬‭3‬‭=10‬
‭2‬ ‭10.4‬ ‭10.6‬ ‭10.5‬
‭PH

‭13‬

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lOMoARcPSD|58579491

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

‭CALCULATIONS‬

‭Mean distance between two legs‬


‭𝐴𝐵‬+‭𝐵𝐶‬+‭𝐶𝐴‬
‭‬‭‭‬‬‭‭‬‭‬‭‬‬‭‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‭‬‬‭‭‬‭𝑙‬ ‬ = ‭3‬
‭= 3 cm‬

‭Mean of h‬‭=‬
(‭0‬.‭555‬+‭0‬.‭6)‭
‭2‬
‬ ‬‭‬‭‬‭‬‭‬
‭= 0.5775‬‭cm‬

‭To find the radius of curvature of the convex lens:‬


‭2‬
𝑙‭ ‬ ‭‬

‭𝑅‬ = + = ‭2‬. ‭8861‬‭‭𝑐‬ 𝑚‬


‭6‬‭ℎ‬ ‭2‬
CS
‭Measurement of refractive indices of water and oil‬
I
YS
‭PH

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

‭ ‬
𝑅 ‭2‬.‭8861‬
µ‭1‬ = ‭1‬ + ‭𝑓‬‭2‬
= ‭‭1
‬ ‬+ ‭34‬.‭7‬
= ‭1‬. ‭0831‬‭‬

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

‭ ‬
𝑅 ‭2‬.‭8861‬
µ‭2‬ = ‭1‬ + ‭𝑓‬‭3‬
= ‭‭1
‬ ‬+ ‭10‬
= ‭1‬. ‭2886‬

‭14‬

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lOMoARcPSD|58579491

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

‭Results‬

‭The refractive index of‬‭water is µ‬‭1‬‭= 1.0831‬

‭The refractive index of‬‭oil is µ‬‭2‬ ‭= 1.2886‬


‭PRECAUTIONS‬
I CS
YS

‭1.‬ T‭ he plane mirror should be clean and fully shining‬


‭surface.‬
‭PH

‭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.‬
‭15‬

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lOMoARcPSD|58579491

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

‭SOURCES OF ERROR‬

‭ .‬ L‭ iquid may not be quite transparent.‬


1
‭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.‬


I CS
YS
‭PH

‭16‬

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lOMoARcPSD|58579491

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

‭BIBLIOGRAPHY‬

‭ ‬‭HELP FROM TEACHERS‬



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


I CS
YS
‭PH

‭17‬

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lOMoARcPSD|58579491

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