The correct relation between the radius of curvature R and focal length f of a spherical mirror is

In geometric optics, the relationship between the radius of curvature (R) and the focal length (f) of a spherical mirror is defined by the formula R = 2f. The radius of curvature is the radius of the sphere from which the mirror is cut, and the center of this sphere is the center of curvature (C). The principal focus (F) is the point where parallel rays converge or appear to diverge after reflection, and the distance from the pole (P) to this focus is the focal length [1]. Geometrically, for mirrors with small apertures, the focus lies exactly midway between the pole and the center of curvature. Consequently, the distance from the pole to the center of curvature (R) is twice the distance from the pole to the focus (f). This fundamental relation is applicable to both concave and convex spherical mirrors.

Sources

1. [1] Science , class X (NCERT 2025 ed.) > Chapter 9: Light – Reflection and Refraction > 9.2.4 Mirror Formula and Magnification > p. 143