Prove that R = 2F for spherical mirrors.
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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
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