Q. A lens of refractive index $n$ is put in a liquid of refractive index $n^{'}.\ $If focal length of lens in air is $f,$ its focal length in liquid will be
A) $\frac{fn^{'}(n - 1)}{n^{'} - n}$
B) $\frac{f(n' - n)}{n^{'}(n - 1)}$
C) $\frac{n^{'}(n - 1)}{{f(n}^{'} - n)}$
D) $\frac{fn'n}{n^{\ }–n'}$
Explanation
(a) $\frac{1}{f} = \left( \frac{n}{1} - 1 \right)\left( \frac{1}{R_{1}} - \frac{1}{R_{2}} \right)$
$\frac{1}{f_{1}} = \left( \frac{n}{n'} - 1 \right)\left( \frac{1}{R_{1}} - \frac{1}{R_{2}} \right)$
Dividing,$\ \ \frac{f_{1}}{f} = \frac{(n - 1)n^{'}}{n - n^{'}}$
Or $f_{1} = - \frac{fn^{'}(n - 1)}{n^{'} - n}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.