Question

The distance between the virtual image from its real object is $60 \, cm$ in case of a concave mirror and the image formed is $3$ times magnified. What is the magnitude of focal length (in $\text{cm}$ ) of the mirror?

Answer 1

$x \, + \, 3x=60 \, \Rightarrow x=15 \, cm$
$u=-15 \, cm$
$m=+ \, 3$
$\therefore \, m=\frac{f}{f - u}\Rightarrow \, + \, 3=\frac{f}{f - \left(\right. - 15 \left.\right)}$
$\therefore \, 3f+ \, 45=f \, \Rightarrow f=- \, 22.5 \, cm$
$\left|f\right|=22.5cm$