Question

A boy standing in front of a concave mirror of focal length $20\text{m}$ moves $2\text{m}$ towards the mirror. What is the distance moved by his image if he is initially standing at a distance of $25\text{m}$ from the pole of the mirror?

• A. $153.33\text{m}$ towards the mirror
• B. $53.33\text{m}$ towards the mirror
• C. $153.33\text{m}$ away from the mirror
• D. $53.33\text{m}$ away from the mirror

Answer 1

The correct option is D $53.33\text{m}$ away from the mirror

Given,
object distance, $u=-25\text{m}$
focal length, $f=-20\text{m}$
image distance, $v=\frac{uf}{u-f}$
$⟹v=\frac{-25\times -20}{-25-(-20)}$
$⟹v=-100\text{m}$
the boy has moved $2\text{m}$ towards the mirror
$⟹u^{{}^{\prime }}=25-2=23\text{m}$
image distance, $v=\frac{uf}{u-f}$
$⟹v=\frac{-23\times -20}{-23-(-20)}$
$⟹v=-153.33\text{m}$
distance moved by the image $=-153.33-(-100)=-53.33\text{m}$
$⟹53.33\text{m}$ away from the mirror.