Question

What is the relation between the focal length and the radius of curvature?

Answer 1

1. The focal length (f) is the distance between the pole (P) and focus(F) of a mirror/lens.
2. The radius of curvature (R) is the distance between the center of a circle to any other point on the circumference of the circle or surface of the sphere.
3. It is observed that the focal length (f) is equal to half of the radius of curvature (R).

R = 2f

Where R = radius of curvature and f = focal length

Or, $f=\frac{R}{2}$

Hence, the focal length is half of its radius of curvature.