Question

Prove that R = 2F for spherical mirrors.​

Answer 1

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Explanation:

Answer 2

Answer:

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