Karmendu Prakash, a student of class XII, conducted an experiment to find the refractive indices of water and oil under the guidance of his physics teacher Mr. Anil Sharma. The experiment involved using a plane mirror, convex lens of known refractive index, and an adjustable needle to measure the focal lengths of the lens alone and in combination with water and oil layers. Measurements were recorded and calculations were performed to determine the refractive indices of water as 1.3342 and oil as 1.44. Precautions taken and potential sources of error in the experiment are also outlined.

2. Name :- Karmendu Prakash
Class :- XII
Section :- B
Roll no. :- 12221
Board roll no. :-
School Name :- Rajkiya Pratibha Vikas Vidyalaya,
Surajmal Vihar
“Under the guidance
of” Mr. Anil Sharma Sir

3. To find the refractive indeces of
‘water’ & ‘oil’

4. It would be my pleasure to express my sincereThanks to My Physics Teacher "Mr. Anil
Sharma Sir" In providing a helping hand in this project Their valuable guidance,
support and supervision all through This project titled
To find the refractive Indices of 'water' & 'oil’
Are responsible for attaining its present form.
Karmendu Prakash
Xii- D
ACKNOWLEDGEMENT

5. CERTIFICATE
It is hereby to certify that, the original and genuine
investigation work has been carried out to investigate
about the subject matter and the related data
collection and investigation has been completed solely,
sincerely and satisfactorily by KARMENDU of Class
'XII-B' Rajkiya Pratibha Vikas Vidyalaya, Surajmal
regarding his project titled
“To find the refractive indices of
“water” & “oil”

6. CONTENTS
1. AIM
2. APPARATUS
3. THEORY
4. PROCEDURE
5. DIAGRAM...
6. OBSERVATION
7. CALCULATION
8. RESULT
9. PRECAUTIONS
10. SOURCES OF ERROR
11. BIBLOGRAPHY

7. AIM
 To find the refractive indices of (a) water(b) oil (Kerosene) using a plane mirror,
a equiconvex lens, (made from a glass of known refractive index) and an
adjustable object needle.
#Clamp
# A plane mirror
# Kerosene oil
# A convex lens
#An optical needle
#Stand, knitting needle
#Plumb line9/24
#Half meter scale
# Glass slab
# A spherometer
APPARATUS REQUIRED

8. THEORY
Let's add small amount of water on a flat, plane surface and place aconvex lens
over it. This forms a plano-concave lens of water between the lower surface of
convex lens and plane mirror.Let f1 and f2 are the focal lengths of water lens and
convex lens respectively, then focal length of the combination is:
1/F = 1/f1 + 1/f2
The focal length of the plano-concave lens is,
1 f1 = 1/F - 1 f2 ***(l)
,

9. From Lens Maker's formula,
1/f_{1} = (μ - 1)(1/R_{1} - 1/R_{2}) = (mu - 1)
• 1/R10/24R
• * 1 = R and R
• * 2 = ∞ for water lens. The refractive index of water is
=1+ R/f_{1} ...
where:- µ = Refractive index of the liquit and 'R' is the
radius of curvature of the lower surface of the convex
lens.
The Radius of curvature of the lens, is
R = 1/2 + 1/2 6h h ..(iii)
Here, I is the average distance between the legs of
spherometer and h is the difference in the reading of the
spherometer when placed first on convex lens and then
on a plane mirror.

11. PROCEDURE
For focal length of convex lens:
1. First find rough focal length of convex lens.
2. Put 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 in such a
manner that there is no parallax between tip of the needle and its image (the tip
of needle appears touching the tip of its image)
4. Note down the 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.13/24Take the mean of these two
readings. This mean distance will be equal to the focal length of the convex lens
(f1).For focal length of the combination
5. Put a few drops of water on the place mirror andplace the convex lens over it
with its same faceabove as before. The water spreads in the form of a layer and
acts like a plano-concave lens as shown in the given figure.

13. 6. Repeat the steps 3 and 4 to find the equivalent focal length of combination.
7. Note the observation as suggested in table.
8. Redo the steps 5, 6, 7 for other transparent liquid (kerosene oil).# For radius of
curvature of convex lens surface:
9. Find the pitch and the least count of the spherometer.
10.Remove the convex lens and dry it completely.
11.Place the spherometer on the lens surface.
12. Place all the three legs of spherometersymmetrically on the lens and adjust
the central screw tip just to touch the surface of the lens.
13. Remove the spherometer from the surface of lens and place it on the plane
mirror and turn the central screw so that its tip touches the plane mirror
surface. Record the readings as suggested in Table 2.15/241
14. Follow the steps 10 and 11 three more times.
15.Get the impressions of three legs ofspherometer, on paper and mark them and
their average distance.

15. OBSERVATION
 PITCH = Distance covered / no. of complete rotations
= 1 mm
 Least Count = Pitch / no. of divisions on head scale
= 1/00
= 0.01 mm
Distance between legs
L1 = 3 cm
L2 = 3 cm
L3 = 3 cm

16. Table 1 – to find focal length of lens and combination
Observation Distance of needle Tip Focal
lenghth x
(cm)
From lens
surface l1 (x
cm)
From plane
mirror l2 (x cm)
Mean = x1 + x2
/ 2
Without liquid 19.9 20 19.95 f = 19.95
With water 29.7 30.1 29.9 f = 29.9
With other
transparent liquid
(kerosene)|
13.82 13.92 13.87 f = 27.25

17. TABLE 2 – to find h
S.No. Initial C.S.R
on convex
lens
No. of
complete
rotations (n)
Final C.S.R.
on plane
mirror
surfaces (b)
m = (a-b) If
a>b =
(100+a-b) If
a<b
h = n x pitch
+ m x L.C.
1 80 0 5 75 0.75
2 79 0 3 76 0.76
3 81 0 7 74 0.74
h= 0.75 mm
h = 0.075 cm

18. Calculation
# The focal length of plano-concave lens
Water (f) :-
1/f_{2} = 1/f_{1} + 1/f_{w} f_{w} = 59.94
(2) Kerosene Oil (f_{o}) :-
1/f_{3} = 1/f_{1} + 1/f_{0} f =45.52
Mean distance between two legs(4):-
l = L1+L2+I3 / 3 =3 cm
Mean h = 0.075cm

19. #To find the radius of curvature of the convex lens
R = (l ^ 2)/(6h) + h/2 = 20.03 cm
Measurement of refractive indices of water and oil
With water between the convex lens and the plane mirror:
μ =1+ R = 1+ 20.03 cm 59.94 cm
=1+0.334
= 1.3342
2) With oil(kerosene) between the convex lens and the
plane mirror:
μs=1+ R fo = 1 +20.03 cm45.52 cm
= 1 + 0.44
= 1.44

20. PRECAUTIONS
1. Make sure the plane mirror is a clean and fully shining surface.
2. The liquid taken must be transparent.
3. Remove the parallax tip to tip.
4. Ensure that the eye remains 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 remains thick.
6. The legs of spherometer should be vertical.
7. Make sure the centre leg of spherometer is turned in one direction only.21/24

21. SOURCES OF ERROR
 The distances x, and x, may not be measured correctly.
 The value of h and I may not be correct.
 Parallax may not be removed properly.
 Back-lash error may be acting on the spherometer.
 The Screw may have friction

22. BIBLIOGRAPHY
 LABORATORY MANUAL OF PHYSICS By - RohitPhysics
 NCERT Textbook for class XII
 Website :-
www.wikipedia.com
www.youtube.com
www.google.com
www.learncbse.in

23. TEACHER’S REMARK