Define the term 'focal length ofa mirror. With the help of a ray diagram, obtain the relation between its focal length and radius of curvature.

Explanation

Distance between principal focus and pole of a mirror is called its focal length. Let C be the centre of curvature of a spherical mirror. Consider a ray OM travelling parallel to the principal axis of mirror and incident at a point M. Obviously CM is normal at M. The reflected ray passes through the focus point. Let MD be the perpendicular drawn from M principal axis of mirror. If angle of incidence `angleOMC =theta,` then `angleCMF= angleMCF=theta` and `angleMFD = 2theta`.
For a mirror of small aperture `theta` = tan `theta` = and `2 theta`
`= tan 2 theta = (MD)/(FD) `
`implies (MD)/(FD)= (2MD)/(CD) implies (1)/(FD)=(2)/(CD) implies FD = (CD)/(2)`
For small aperture the point D is very close to pole P and so we have
`FP = (CP)/(2) or f = (R )/(2) or R = 2f `.