Question

A concave mirror for face viewing has a 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. $0.16\text{m}$
• B. $1.6\text{m}$
• C. $0.32\text{m}$
• D. $0.24\text{m}$

Answer 1

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

Given
$f=-0.4\text{m},\text{Let}u=-x,v=ym=5=\left(\frac{-v}{u}\right)=\left(\frac{y}{-x}\right)$
$\Rightarrow y=5x$
Using Mirror formula
$\left(\frac{1}{f}\right)=\left(\frac{1}{v}\right)+\left(\frac{1}{u}\right)$
$\Rightarrow \left(\frac{1}{-0.4}\right)=\left(\frac{1}{5x}\right)+\left(\frac{1}{-x}\right)=\frac{4}{-5x}$
$x=-0.32\text{m}$
So, object is at a distance of $0.32\text{m},$ infront of the mirror