Question

A concave mirror for face viewing has focal length of $0.4\text{m}$. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of $5$ is

• A. $0.32\text{m}$
• B. $1.60\text{m}$
• C. $0.16\text{m}$
• D. $0.24\text{m}$

Answer 1

The correct option is A $0.32\text{m}$

Given:
Focal length $f=0.4\text{m}$
Magnification $m=5$
We know that magnification
$m=-\frac{v}{u}$
$\Rightarrow +5=-\frac{v}{u}$
$\Rightarrow v=-5u$
Using mirrors formula
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{-5u}+\frac{1}{u}=\frac{-1}{0.4}$
$\therefore u=-0.32\text{m}$
Hence option $\left(C\right)$ is correct.