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.
