Question

A concave mirror of focal length \( f \) in air is dipped in a liquid of refractive index \( \mu \). Its focal length in the liquid will be:

• A. \( \frac{f}{\mu} \)
• B. \( \frac{f}{(\mu - 1)} \)
• C. \( \mu f \)
• D. \( f \)

Hint:

The focal length of a mirror is not affected by the refractive index of the medium, unlike lenses where the focal length changes with the refractive index of the medium.

Answer 1

The Correct Option is D

The question asks about the focal length of a concave mirror when it is dipped in a liquid of refractive index \( \mu \). The key concept to understand here is how the properties of a mirror differ from those of a lens regarding the effect of a medium’s refractive index.

Concept: 

A mirror forms images by reflecting light rather than refracting it. Thus, the change in the surrounding medium does not affect the focal length of a mirror. The focal length of mirrors remains constant irrespective of the surrounding medium, unlike lenses where the focal length changes when immersed in a different medium.

Explanation:

1. The focal length of a mirror is determined solely by its geometry, specifically its curvature, according to the formula for a spherical mirror:

\(f = \frac{R}{2}\)

1. Here, \( R \) is the radius of curvature of the mirror. Since refractive index \( \mu \) does not appear in this formula, it indicates that the refractive index of the medium does not affect the focal length of the mirror.

Conclusion:

1. Therefore, the focal length of a concave mirror remains the same even when it is placed in a medium with a different refractive index.
2. Thus, the correct answer is \( f \).

Hence, the correct choice is:

\( f \)

Answer 2

The focal length of a concave mirror is independent of the refractive index of the surrounding medium. It depends only on the curvature of the mirror. Therefore, when the mirror is dipped in a liquid with refractive index \( \mu \), the focal length remains the same as in air. Thus, the focal length in the liquid is: \[ \boxed{f}. \]