Question

A double convex lens $(\mu =3/2)$ of focal length $20cm$ is totally immersed in water $(\mu =4/3)$. Its focal length now will be :

• A. $20cm$
• B. $30cm$
• C. $40cm$
• D. $10cm$

Answer 1

The correct option is B $30cm$

From lens formula

$\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$

If focal length of lens in air is $f_a$ and in liquid is $f_l$, then

$\frac{1}{f_a}=({}_a{\mu }_g-1)(\frac{1}{R_1}-\frac{1}{R_2})$

$\frac{1}{f_e}=({}_l{\mu }_g-1)(\frac{1}{R_1}-\frac{1}{R_2})$

$\frac{f_l}{f_a}=\frac{({}_a{\mu }_g-1)}{({}_l{\mu }_g-1)}$

$\frac{f_l}{20}=\left[\frac{\frac{3}{2}-1}{\frac{4}{3}-1}\right]$

$=\frac{3}{2}$

$f_l=30cm$