Question

Prove that for a concave mirror, the radius of curvature is twice the focal length for small aperture as compare to its radius of curvature.

Answer 1

(i)

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)

Hence, ∠MCF = ∠CMF

So, CF = MF

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

CF = FP

PC = 2PF

C = 2f

or \(f=\frac{C}{2}\)

Hence proved.