Question

At what distance (in m) from a convex mirror of focal length $2.5m$ 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.

Answer 1

Answer: 2.5

We have,
$m=-\frac{v}{u}=\frac{1}{2}$
$v=-\frac{u}{2}$
$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$
$\frac{1}{u}+\frac{1}{-u/2}=\frac{1}{2.5m}$
$-\frac{1}{u}=\frac{1}{2.5m}$
$u=-2.5m$
Thus, he should stand at a distance of $2.5m$ from the mirror.