The distance between the pole and the center of curvature of a spherical mirror, in terms of its focal length f, is equal to __________.

Correct option is D

In a spherical mirror (either concave or convex), the distance between the pole (P) and the center of curvature (C) is equal to 2f, where $f$ is the focal length of the mirror. The center of curvature is the point on the principal axis where the spherical mirror’s curvature would form a complete circle, while the focal point (F) is halfway between the pole and the center of curvature. This relationship is derived from the mirror formula and basic properties of spherical mirrors.

For any spherical mirror:

$$PC=2\times PF=2f$$

Important Key Points:

1. The focal length $f$ is half the distance between the pole and the center of curvature.
2. $PC=2f$ is a fundamental property of spherical mirrors.
3. This rule applies to both concave and convex mirrors.
4. In a concave mirror, the focal point lies between the pole and the mirror’s surface.
5. For a convex mirror, the focal point is virtual and appears behind the mirror.
6. Understanding focal length is essential for applications involving mirrors and optics.