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:
Answer & explanation
Correct answer: option 4
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
$f_{\text{water}} = 72 \text{ cm}$