Focal Length and Radius for Spherical Mirror

Description:

Relation between radius of curvature and focal length is given by −

f = R/2

Proof

Ray parallel to the principle axis strike at a point ‘A’ on the mirror.

To make a normal at any point on the spherical mirror a line passing through center of curvature is taken.

As per the rules of reflection: angle of incidence = angle of reflection

∠i = ∠r ........(1)

As OA and CP are parallel to each other, we get

∠ACF = i

And

∠FCA = i ............ from eq.1

∴ ∠ACF = ∠FCA = i

∴ CF = FA

When incident ray comes closer to principle axis FA = FP

∴ CF = FP

Then,

R = CP

R = CF + FP

R = f + f

∴ R = 2f