Question

For spherical mirror the relationship between radius of curvature R and focal length is

• A. F=2R
• B. R=2F
• C. R=\(\frac{f}{2}\)
• D. F=\(\frac{R}{2}\)

Answer 1

The Correct Option is B, D

We need to determine the relationship between the radius of curvature \( R \) and the focal length \( f \) for a spherical mirror.

1. Understanding Spherical Mirrors:
A spherical mirror (concave or convex) has a reflecting surface that forms part of a sphere. The radius of curvature \( R \) is the radius of this sphere, and the focal length \( f \) is the distance from the mirror’s pole to the focal point, where parallel rays converge or appear to diverge after reflection.

2. Deriving the Relationship:
For a spherical mirror, the focal point lies halfway between the pole and the center of curvature. Geometrically, the focal length is half the radius of curvature. This can be derived using the mirror formula and paraxial ray approximations, but the standard result is:

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

3. Applicability:
This relationship holds for both concave and convex mirrors, where \( R \) and \( f \) are positive for concave mirrors and negative for convex mirrors in the sign convention.

Final Answer:
The relationship between the radius of curvature \( R \) and the focal length \( f \) for a spherical mirror is:

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