There is an equiconvex glass lens with radius of each face as R and a μ g = 3 2 a n d a μ w = 4 3 . If there is water in object space and air in image space, then the focal length is Options: A . &nbsp2R B . &nbspR C . &nbsp3R2 D . &nbspR2

There is an equiconvex glass lens with radius of each face as R and aμg=32and

Question

There is an equiconvex glass lens with radius of each face as R and

_{a} μ_{g} = \frac{3}{2} a n d_{a} μ_{w} = \frac{4}{3}

. If there is water in object space and air in image space, then the focal length is

Options:

A . 2R

B . R

C . 3R2

D . R2

Answer: Option C
:
C
Consider the refraction of the first surface i.e. refraction from rarer medium to denser medium

\frac{μ_{2} - μ_{1}}{R} = \frac{μ_{1}}{- u} + \frac{μ_{2}}{v_{1}} \Rightarrow \frac{(\frac{3}{2}) - (\frac{4}{3})}{R} = \frac{\frac{4}{3}}{\infty} + \frac{\frac{3}{2}}{v_{1}} \Rightarrow v_{1} = 9 R

Now consider the refraction at the second surface of the lens i.e. refraction from denser medium to rarer medium

\frac{1 - \frac{3}{2}}{- R} = - \frac{\frac{3}{2}}{9 R} + \frac{1}{v_{2}} \Rightarrow v_{2} = (\frac{3}{2}) R

The image will be formed at a distance of

\frac{3}{2} R

.This is equal to the focal length of the lens.

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