An observer whose least distance of distinct vision is d , views his own face in a convex mirror of radius of curvature r . The magnification produced can not exceed?

Step-by-step solution

Magnification, ​ m = f f - u ⇒ m = f f + x m = r / 2 r / 2 + x ⇒ m = r r + 2 x ------- 1 from mirror formula 1 v + 1 u = 1 f ⇒ 1 ( d - x ) + 1 - x = 1 f ⇒ 1 d - x - 1 x = 2 r + x - ( d - x ) x ( d - x ) = 2 r ⇒ 2 x - d r = 2 x d - x 2rx - rd = 2xd - 2x 2 ⇒ 2x 2 + 2(r - d)x - rd = 0 2 x 2 + 2 r - d x - r d = 0 ⇒ x = - 2 r - d ± 4 r - d 2 + 8 r d 4 x = 2 d - r ± 4 r 2 + d 2 4 ⇒ x = d - r ± r 2 + d 2 2 2 x = d - r ± r 2 + d 2 putting the value of x in equation (1) m = r r + [ d - r ± r 2 + d 2 ] For m to be maximum, x