The distance between the focus and the centre of curvature of  spherical mirror in terms of the radius of curvature R is equal to:

Correct option is B

Ans. (b) R/2

Explanation:

• For a spherical mirror, the radius of curvature (R) is the distance between the center of curvature (C) and the mirror’s surface. The focus (F) is the point where parallel rays of light either converge (concave mirror) or appear to diverge from (convex mirror) after reflecting off the mirror.

• The distance between the focus (F) and the center of curvature (C) is known as the focal length (f) of the mirror. For any spherical mirror, the focal length $f$ is related to the radius of curvature $R$ by the formula:

  $$f=R/2$$

• Thus, the distance between the focus and the center of curvature is R/2.

Important Key Points:

1. Focal length (f) of a spherical mirror is half of the radius of curvature (R).
2. For concave mirrors, the focus lies between the pole (P) and the center of curvature (C).
3. This relationship $f=R/2$applies to both concave and convex mirrors.
4. Center of curvature (C) is the center of the sphere from which the mirror segment is derived.
5. The focus (F) is where parallel rays converge (concave) or appear to diverge (convex).
6. This concept is fundamental to understanding mirror equations and image formation.

Information Booster:

• Radius of Curvature (R): The distance from the mirror’s surface to the center of curvature.
• Focal Length (f): Half the radius of curvature for spherical mirrors, determining where light rays focus.
• Mirror Equation: Used to find image positions and magnifications in mirror setups, given by 1f=1v+1u\frac{1}{f} = \frac{1}{v} + \frac{1}{u}  1/f=1/u + 1/v, where $u$ and $v$ are object and image distances respectively.