A boy of height 1 m stands infront of a convex mirror. His distance from the mirror is equal to the focal length of the mirror, the height of the image is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0.50 m
The mirror equation for spherical mirror,
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
Given, $u=-f$
$\frac{1}{f}=\frac{1}{v}-\frac{1}{f}$
$⇒\frac{1}{v}=\frac{1}{2f}$
$⇒v=2f$
Magnification, $m=\frac{-v}{u}=\frac{-2f}{f}=-2$
and,
$m=\frac{h'}{h}=-2$
$⇒h'=-2m$
Since convex mirrors always produce images with magnification less than 1,
$m=\frac{f}{f+u}=\frac{f}{f+f}=\frac{f}{2f}=\frac{1}{2}$
$h'=m×h=\frac{1}{2}×1=0.5m$