11 refractive index using concave mirror

AIM :
To find refractive index of any liquid (water) using a concave mirror.
APPARATUS:
A concave spherical mirror, water, an optical needle, a clamp stand, one meter scale, plumb line, etc.
THEORY:
If the tip of object needle 0 be at the centre of curvature C, tip of image will exactly coincide with it. (Principle axis is verticle to the plane).
When water is filled in concave mirror, object needle is again replaced to move to C' to remove parallax between tips of object needle and its image.
A ray starting from C will reach at E without deviation because it is along radius of curvature.
Due to water in the concave mirror the position of object and image shifts to C' i.e., now ray starting fromC' after refraction moves along ED and then DC to make apparent image of centre of curtature.
Image

Object Needle
I
I
I
I

I
I

I
I
I
I
I
I

N

/

I
I
I

I
I

I

I

I.
II

I

I
I

B

Fig. 1 : Refractive index of liquid
.. LNDC'

=

i (angel of incidence)

=

LBC'D

LMDE

=

r (angel of refraction)

=

LBCD

sin i
= sin r

allw

In LillC'D, sin i

=

~BCD sin r

=

DBIDC'

DC

DBIDC

DC'

DB
DC'

DB
DC

For normal view, D will be near B. therefore allw

=

BC
BC'

If small quantity of water in concave mirror B will be very near to P i.e.,
BC .:::PC and BC' .:::PC'
PC
allw

Real radius of curvature of mirror

= PC' = Apparent radius of curvature of mirror

PROCEDURE :
(i) Place the concave mirror on a horizontal surface (plane) so that its principle axis is along vertical. (ii) Hold the optical needle horizontally in a clamp stand so that its tip lies just above the pole
'P' and at a distance equal to 2f (f is focal length) as shown in figure 1.
(iii)

Remove the parallex between the needle and its image.

(iv)

Mark the real and inverted image of the optical needle in the mirror. Note the reading of this image.

(v) Measure the distance (PC) using plumb line and metre scale.
(vi) This measured distance is the actual radius of curvature of the concave mirror.
(vii)

Now add