A convex lens of glass (n = 1.5) has a focal length 18 cm in air. When it is immersed in water (n = 4/3), the focal length increases to:

54 cm

The correct answer is Option (3) → 54 cm

To determine the new focal length of a convex lens immersed in water,

$\frac{1}{f}=(n_{lens}-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$

$n_{lens}=1.5$ and $f_{air}=18cm$

$\frac{1}{18}=(1.5-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$

$\left(\frac{1}{R_1}-\frac{1}{R_2}\right)=\frac{1}{9}$

$∴\frac{1}{f_{water}}=(n_{lens}-n_{medium})\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$

$=(1.5-\frac{4}{3})(\frac{1}{9})=(\frac{9-8}{6})(\frac{1}{9})$

$⇒f_{water}=54cm$