Question

A convex lens having refractive index 1.6 has focal length 12 cm, when it is in air. The focal length of that lens when placed in water is (refractive index of water = 1.28)

• A. \(655 \text{mm}\)
• B. \(288 \text{mm}\)
• C. \(555 \text{mm}\)
• D. \(355 \text{mm}\)

Hint:

Use the lens maker formula in both media and take the ratio.

Answer 1

The Correct Option is B

Step 1: Lens maker formula
In a medium, \(\frac1f = \left(\frac{n_l}{n_m}-1\right)\left(\frac1{R_1}-\frac1{R_2}\right)\).

Step 2: Air and water
In air, \(\frac1{12} = (1.6-1)K = 0.6K\). In water, \(\frac1{f_w} = \left(\frac{1.6}{1.28}-1\right)K = 0.25K\).

Step 3: Ratio
\(\frac{f_w}{12} = \frac{0.6}{0.25} = 2.4\), so \(f_w = 28.8\ \text{cm} = 288\ \text{mm}\). Option (B).

Final Answer:
The focal length in water is 288 mm. \[ \boxed{\text{(B)}\ 288\ \text{mm}} \]