The correct relation between the radius of curvature (R) and focal length (f) of a spherical mirror is given by option 2, which states that R is equal to 2f.

To understand this, we need to first understand the concept of a spherical mirror. A spherical mirror is a mirror with a curved surface, either convex or concave. The curvature of the mirror is determined by its radius of curvature, which is the radius of the sphere from which the mirror is formed.

In a spherical mirror, light rays that are parallel to the principal axis converge or diverge after reflecting off the mirror. The point where these rays converge or appear to diverge from is known as the focal point. The distance from the mirror`s surface to the focal point is called the focal length.

The correct relation between R and f can be understood by considering the geometry of the mirror. For a concave mirror, where the reflecting surface curves inward, the focal point is located between the mirror and the center of curvature. In this case, the focal length is positive, and R is twice the focal length. Hence, R = 2f.

Therefore, the correct answer is option 2, R = 2f.