At what distance (in m ) from a convex mirror of focal length 2.5 m should a boy stand so that his image has a height equal to half of his height? The principal axis of the mirror is perpendicular to the height of the boy.

Step-by-step solution

We have, m = - v u = 1 2 v = - u 2 1 u ⁡ + 1 v ⁡ = 1 f ⁡ 1 u ⁡ + 1 - u ⁡ / 2 = 1 2 . 5   m - 1 u ⁡ = 1 2 . 5  m u ⁡ = - 2 . 5  m Thus, he should stand at a distance of 2.5   m from the mirror.