Question

A lens of refractive index $n$ is put in a liquid of refractive index $\left( n ^{\prime}\right),$ if focal length of lens in air is ' $f$ ', its focal length in liquid will be:

• A. $\frac{-f n'(n-1)}{n'-n}$
• B. $\frac{-f\left(n'-n\right)}{n'(n-1)}$
• C. $\frac{-n'(n-1)}{f\left(n'-n\right)}$
• D. $\frac{f n' n}{n-n'}$

Answer 1

Answer: (A)

$\frac{1}{f}=\left(\frac{n}{1}-1\right)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)$
$\frac{1}{f_{l}}-\left(\frac{n}{n'}-1\right)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)$
$\frac{f_{l}}{f}=\frac{(n-1) n'}{n-n'}$ or $f_{l}=\frac{-f n'(n-1)}{n'-n}$