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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, BF = PF

or FC = FP = PF

or PC = PF + FC = PF + PF

or R = 2 PF = 2f

or F=R/2

or 2F=R

Hope this helps............

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Q: How do you derive relation between focal length and radius of curvature of concave mirror?
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