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:

72 cm

The correct answer is Option (4) → 72 cm

Use lens maker formula in a medium:

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

Step 1: In air

$\frac{1}{f_{\text{air}}} = (1.5 - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) = 0.5 \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$

Given $f_{\text{air}} = 18$ cm:

$\frac{1}{18} = 0.5 \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$

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

Step 2: In water

$\frac{1}{f_{\text{water}}} = \left( \frac{1.5}{4/3} - 1 \right) \left( \frac{1}{9} \right)$

$= (1.125 - 1) \left( \frac{1}{9} \right) = 0.125 \times \frac{1}{9} = \frac{1}{72}$

Step 3: Final answer

$f_{\text{water}} = 72 \text{ cm}$