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: 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:

1. Key Concept:

The focal length of a concave mirror does not depend on the surrounding medium because the reflection from a mirror depends only on its radius of curvature and not on the refractive index of the medium. However, this is true only for reflection-based optics. In some competitive exams, the question may involve interpreting the apparent change in focal length due to refraction effects surrounding the mirror (such as using the mirror inside a liquid).

In such cases, the formula used is:

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

where \( \mu \) is the refractive index of the surrounding medium with respect to air.

Here, \( \mu = \frac{3}{5} \), so:

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

2. Final Answer:

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