Question

A concave mirror of radius 30 cm is placed in water. It’s focal length in air and water differ by

• A. 15
• B. 20
• C. 30
• D. 0

Answer 1

The Correct Option is D

To determine the difference in the focal length of a concave mirror in air and water, we analyze the given problem.

1. Understanding the Focal Length of a Mirror:
The focal length \( f \) of a spherical mirror (concave or convex) is related to its radius of curvature \( R \) by the formula:
\( f = \frac{R}{2} \)
This relationship depends only on the mirror's geometry and is independent of the medium surrounding the mirror, as reflection does not involve the refractive index of the medium.

2. Given Data:
The radius of curvature of the concave mirror is given as \( R = 30 \, \text{cm} \).

3. Calculating Focal Length:
Using the formula for focal length:
\( f = \frac{30}{2} = 15 \, \text{cm} \)
This focal length applies in both air and water, as the medium does not affect the mirror's focal length.

4. Comparing Focal Lengths:
- In air: \( f_{\text{air}} = 15 \, \text{cm} \)
- In water: \( f_{\text{water}} = 15 \, \text{cm} \)
The difference in focal length is:
\( f_{\text{air}} - f_{\text{water}} = 15 - 15 = 0 \, \text{cm} \)

Final Answer:
The focal length of the concave mirror in air and water differs by \( 0 \, \text{cm} \).