A boy of height $1m$ stands in front of a convex mirror. His distance from the mirror is equal to its focal length. The height of his image is: (Assume paraxial ray approximation holds)

The correct option is D $0.5m$

His distance from the mirror is the

object distance, treating him as an object, So,

Applying mirror formula

$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$

Here, u is negative and f for convex

mirror is positive , So,

$\frac{1}{-f}+\frac{1}{v}=\frac{1}{f}$

$\frac{1}{v}=\frac{2}{f}$

Also, m(magnification) $=\frac{-v}{u}$

$m={\left[\frac{-\frac{2}{f}}{-\left(\frac{1}{f}\right)}\right]}^{-1}=\frac{1}{2}$

We know,

$m=\frac{imagelength}{objectlength}$

Here, object length = Boy's height = 1 m.

So,

$m=\frac{imagelength}{1m}=\frac{1}{2}$

$\Rightarrow$ image length = $\frac{1}{2}=0.5m$

Option - C is correct.