Question

write down the relation between focal length and radius of curvature of convex mirror

Answer 1

focal length is half the radius of curvature

Answer 2

Ray parallel to the principle axis strike at a point ‘A’ on the mirror.To make a normal at any point on the spherical mirrora line passing through center of curvature is taken.As per the rules of reflection: angle of incidence = angle of reflection∠i = ∠r ........(1)As OA and CP are parallel to each other, we get∠ACF = iAnd∠FCA = i ............ from eq.1∴ ∠ACF = ∠FCA = i∴ CF = FAWhen incident ray comes closer to principle axis FA = FP∴ CF = FPThen,R = CPR = CF + FPR = f + f∴ R = 2f