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.

Question

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.,

MARKS App · Accepted Answer

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.

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