Answer to Question #170569 in Optics for Innocent

Question

Show that the radius of curvature of a mirror is twice the focal length

Answer 1

Let us consider MM’ as small aperture concave mirror. The line through centre of curvature C is perpendicular to the mirror.

Applying law of reflections:

∠OMC = ∠CMF (angle of incidence = angle of reflection)

∠MCF = ∠OMC (alternate angle)

∠MCF = ∠CMF

CF = MF

Since aperture of mirror is very small, M is very near P and we can put

CF = FP

PC = 2PF

C = 2f

$f= \frac{C}{2}$