Optics Question 126

Question: There is an equiconvex glass lens with radius of each face as R and $ _{a}{\mu _{g}}=3/2 $ and $ _{a}{\mu _{w}}=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) 3 R/2

D) $ R^{2} $

Show Answer

Answer:

Correct Answer: C

Solution:

Consider the refraction of the first surface i.e. refraction from rarer medium to denser medium

$ \frac{{\mu _{2}}-{\mu _{1}}}{R}=\frac{{\mu _{1}}}{-u}+\frac{{\mu _{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}=9R $

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}}{9R}+\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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