Question

derive the equation "R=2f".

Answer 1

Considering a ray of light AB parallel to the principal axis with an incident on the spherical mirror at point B.

The normal to the surface at point B is CB and CP=CB=R which is the radius of the curvature. After reflection the ray AB will diverge through point F in case of a convex mirror or will pass through point F in case of a concave mirror and will obey law of reflection which means that i=r.

From the figure, if the aperture of the mirror is small then, B lies close to P BF=PF Or, FC=FP=PF Or, PC=PF+FP = PF+PF Or, R= 2PF = 2f Or, R = 2F