derived the relatiok between focal length and radius of curvature for spherical mirror
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Answers
The relationship between the focal length f and radius of curvature r is r = 2f.
Consider a ray of light AB, parallel to the principal axis and 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 the law of reflection i.e. i = r.
From the geometry of the figure,
∠BCP = θ = i
In D CBF, θ = r
∴BF = FC (because i = r)
If the aperture of the mirror is small, B lies close to P, and therefore BF = PF
Or FC = FP = PF
Or PC = PF + FC = PF + PF
Or R = 2 PF = 2f
Or f = R/2
Similar relation holds for convex mirror also. In deriving this relation, we have assumed that the aperture of the mirror is small.
