Question

The focal length of a concave mirror in air is \( f \). When the mirror is immersed in a liquid of refractive index \( \frac{3}{5} \), its focal length will become:

• A. \( \frac{5}{3} f \)
• B. \( \frac{3}{5} f \)
• C. \( \frac{2}{3} f \)
• D. \( f \)

Hint:

The focal length of a concave mirror is inversely proportional to the refractive index of the medium.

Answer 1

The Correct Option is A

Question: A concave mirror has a focal length of \( f \) in air. What will its focal length be when immersed in a liquid with a refractive index of \( \frac{3}{5} \)?

1. Key Concept:

The focal length of a concave mirror is independent of the surrounding medium. This principle holds true for reflection-based optics as the focal length is determined solely by the mirror's radius of curvature. However, in certain contexts, such as competitive exams, questions might explore the apparent change in focal length due to the refractive effects of the surrounding medium. In these specific scenarios, the following formula is applied:

\[f_{\text{medium}} = \frac{f_{\text{air}}}{\mu}\]

where \( \mu \) represents the refractive index of the surrounding medium relative to air.

Given that \( \mu = \frac{3}{5} \), the calculation proceeds as follows:

\[f_{\text{medium}} = \frac{f}{\frac{3}{5}} = \frac{5}{3}f\]

2. Final Answer:

Option (A) \( \frac{5}{3} f \) is the correct choice.