Question

A convex lens made of glass has focal length 0.15 m in air. If the refractive index of glass is 3/2 and that of water is 4/3, the focal length of lens when immersed in water is

• A. 0.45 m
• B. 0.15 m
• C. 0.30 m
• D. 0.6 m

Hint:

$f_{water} \approx 4 \times f_{air}$ for a glass lens.

Answer 1

The Correct Option is D

Step 1: Formula
Use the Lens maker's formula: $\frac{1}{f} = (\mu - 1)(\frac{1}{R_1} - \frac{1}{R_2})$.
Step 2: Comparison
In air, $\frac{1}{f_a} = (\frac{3/2}{1} - 1)C = \frac{C}{2}$. In water, $\frac{1}{f_w} = (\frac{3/2}{4/3} - 1)C = \frac{C}{8}$.
Step 3: Result
$\frac{f_w}{f_a} = \frac{C/2}{C/8} = 4$. Therefore, $f_w = 4 \times 0.15 = 0.6$ m.
Final Answer: (d)