Define focal length of a mirror and hence relate focal length and radius of curvature of a mirror.

Explanation

Let us consider a concave mirror of pole P, center of curvature C and focus F. Let the focal length f and radius of curvature R. AM is incident ray, MF is reflected ray and MC is normal
From `DeltaMCP, tan theta= (MP)/(CP)`
From `Delta MFP, tan 2theta = (MP)/(FP)`
Since `theta` is very small `tan theta ~~ theta and tan 2theta ~~ 2 theta`
`therefore = (MP)/(CP)and 2 theta = (MP)/(FP) or theta = (MP)/(2FP)`
`therefore CP= 2FP therefore R= 2f or r = (R )/(2)`