Let C be the centre of curvature of the mirror. Consider a ray parallel to the principal axis striking the mirror at M. Then CM will be perpendicular to the mirror at M. Let θ be the angle of incidence, and MD be the perpendicular from M on the principal axis. Then, ∠MCP = θ and ∠MFP = 2θ.
For small θ, which is true for paraxial rays, tan θ ≈ θ, tan 2θ ≈ 2θ. Therefore, Eq. (1) gives
Now, for small θ, the point D is very close to the point P. Therefore, FD = f and CD = R. Equation (2) then gives f = R/2 ---------- (3)
