Question

At what distance a boy should stand from a convex mirror of focal length $2.5\text{m}$, such that his image has a height equal to half the original height?

• A. $2.5\text{m}$
• B. $3.5\text{m}$
• C. $4.5\text{m}$
• D. $5.5\text{m}$

Answer 1

The correct option is A $2.5\text{m}$

Given:
Height of object, $h_o=h$ $($let$)$
Height of image, $h_i=h/2$
Focal length, $f=+2.5\text{m}$
So, $m=\frac{h_i}{h_o}=\frac{-v}{u}$
$\Rightarrow \frac{h/2}{h}=\frac{-v}{u}$
$\Rightarrow v=\frac{-u}{2}$
Applying mirror formula,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{-1}{u/2}+\frac{1}{u}=\frac{1}{2.5}$
$\Rightarrow \frac{-1}{u}=\frac{1}{2.5}$
$\Rightarrow u=-2.5\text{m}$