As shown in the figure, a paraxial ray is incident
at point Q on a concave mirror.
q = angle of incidence = angle of reflection
= Ð CQF = Ð QCF ( by geometry )
So, for D CFQ,
exterior Ð QFP = Ð CQF + Ð QCF = 2q .
For paraxial incident ray and small aperture,
CP' » CP = R and FP' » FP = f.
For small aperture, 2q is very small.
\ from the figure, 2q »
FP
QP
=
f
QP
… ( 1 ) and q =
CP
QP
=
R
QP
… ( 2 )
From equations ( 1 ) and ( 2 ), R = 2f ⇒ f = R / 2
Thus, focal length of a concave mirror is half its radius of
curvature.