Question

Refractive index of a glass convex lens is 1.5. The radius of curvature of each of the two surfaces of the lens is 40 cm. The ratio of the power of the lens when immersed in a liquid of refractive index 1.25 to that when placed in air is

• A. 2:3
• B. 3:2
• C. 2:5
• D. 5:2

Hint:

Power of a lens decreases when immersed in a medium with refractive index greater than 1.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We use Lens Maker's formula to find the ratio of powers in different media.

Step 2: Key Formula or Approach:
Power \( P = \frac{1}{f} = (\mu_{\text{rel}} - 1) \left[ \frac{1}{R_1} - \frac{1}{R_2} \right] \).
Since the lens geometry is constant, \( P \propto (\mu_{\text{rel}} - 1) \).

Step 3: Detailed Explanation:
1. In air (\( \mu_m = 1 \)):
\( P_{\text{air}} \propto (1.5 - 1) = 0.5 \) \dots (i)
2. In liquid (\( \mu_m = 1.25 \)):
\( \mu_{\text{rel}} = \frac{1.5}{1.25} = 1.2 \)
\( P_{\text{liq}} \propto (1.2 - 1) = 0.2 \) \dots (ii)
Dividing (ii) by (i):
\[ \frac{P_{\text{liq}}}{P_{\text{air}}} = \frac{0.2}{0.5} = \frac{2}{5} \]

Step 4: Final Answer:
The ratio of the powers is \( 2 : 5 \).