Question

prove that :

R = 2f
​

Answer 1

Answer:

Explanation:

Consider a ray of light AB, parallel to the principal axis, incident on a spherical mirror at point B.

The normal to the surface at point B is CB and CP = CB = R, is the radius of curvature.

The ray AB, after reflection from mirror will pass through F (concave mirror) or will appear to diverge from F (convex mirror) and obeys law of reflection, i.e., i = r.  

From the geometry of the figure, if the aperture of the mirror is small, B lies close to P.

Therefore, BF = PF  

or FC = FP = PF  

or PC = PF + FC

        = PF + PF  

or R = 2PF

or R = 2f