Aim:
To find refractive indices of water and turpentine oil using a plane
mirror, a equiconvex lens (made from a glass of known refractive
index) and an adjustable object needle.
Apparatus:
A convex lens, an optical needle, a plane mirror, a clamp stand, a
spherometer, a plumb line, metre scale, water and turpentine oil.
Theory:
Let’s add small amount of water on a flat, plane surface and place a
convex 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:
The focal length of the plano-concave lens is,
(
From Lens Maker’s formula,
=(
R1 = R and R2 =
for water lens.
1
)(
)
…(i)
)
The refractive index of water is ,
…(ii)
(where ‘R’ is the radius of curvature of the concave surfaces of the
plano-concave lens).
The Radius of curvature of the lens, is
…(iii)
Procedure:
I.
For finding the focal length of convex lens:
(i)
Measure the rough focal length of the convex lens.
(ii)
Place the plane mirror with the convex lens placed on it
above the horizontal base of a clamp stand horizontally
as its tip lies vertically above the optical centre of the
lens. Adjust the needle at a height a little more than the
rough focal length of the convex lens.
(iii) Try to remove the parallax between the tip of the object
needle and its image tip.
(iv) Note the distance of the tip of the needle from the
centre of the upper surface of the lens. Let it be x1. (Use
plumb line).
(v)
Remove the convex lens and measure the distance of the
tip of the needle from the plane mirror. Let it be x2. (Use
plumb line).
2
(vi)
II.
Repeat and record all the observations.
For finding the focal length of the plano-concave
lens:
Pour few drops of water over the plane mirror and place the
convex lens over it. Repeat steps (ii) to (iv) as done above.
Repeat the procedure with turpentine oil also.
III. For finding ‘l’:
Determine the pitch and least count of scale of the
spherometer. Place the spherometer on the dried surface of
the convex lens. Turn the screw downwards very gently till
the tip of the screw just touches the lens. Read and record
the reading.
Keep the spherometer’s legs on the base of a paper and
adjusting the central screw, find the pricks A, B and C of the
three legs of the spherometer. Join the centres of the three
pricks and measure the lengths with the half-metre scale.
Note the values of AB, BC and AC.
3
Fig: (a) to find focal length of convex lens
(b) for the length of legs AB, BC, CA of the spherometer
Fig: to find focal length of the plano concave lens
4
Observations
Pitch of the spherometer= 1 cm
Least count of the spherometer = 0.01 cm
Distance between the legs:
(1) AB
(2) BC
(3) CA
= 3 cm
= 3 cm
= 3 cm
Table for calculation of ‘h’
S.No
1
2
Initial
No.
of
reading of complete
the C.S. on rotations
the convex
lens
(n)
(a)
62
0
64
0
Final
Additional h=n x Mean
reading
C.S
div. pitch “h”
of the c.s moved
+mx
on
the
L.C
glass slab
6.5
4
5
55.5
60
0.555 0.5775
0.6
To measure focal length f ‘ of convex lens
Distance of needle tip from
Area
S.No Tip of the upper
Upper
between
surface of the
surface of
lens and
convex lens
the plane
plane mirror
X1
mirror
X2
Without
1
30.5
31
liquid
2
36.7
37.2
With water 1
31.4
31.8
2
37.5
38.1
With oil
1
9.4
9.6
2
10.4
10,6
CALCULATIONS
Mean distance between two legs
=3 cm
Mean h = 0.7557 cm
To find the radius of curvature of the convex lens:
6
Mean
x=
30.75
36.95
31.6
37.8
9.5
10.5
Focal
length
f1=
33.85
f2=34.7
f3=10
Measurement of refractive indices of water and turpentine oil
1) With water between the convex lens and the plane mirror:
2) With turpentine oil between the convex lens and the plane
mirror
Result
The refractive index of water is µ1 = 1.06552
The refractive index of turpentine oil is µ2 = 1.22736
7
Precautions
(i)
The screw of the spherometer should be moved in one
direction only to avoid backlash error.
(ii)
The screw should be moved just to touch the surface of the
convex lens or the glass slab.
(iii) The parallax should be removed properly.
(iv) The lens and the plane mirror should be properly cleaned.
(v)
The convex lens of large focal length should be used.
(vi) The spherometer reading should be taken first on the surface
of the convex lens and then on the glass slab.
Sources of error:
(i)
The distances x1 and x2 may not be measured correctly.
(ii)
The value of h and l may not be correct.
(iii) Parallax may not be removed properly.
(iv) Backlash error may be acting on the spherometer.
8