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Q.
An object is placed at $20\,cm$ in front of a concave mirror produces three times magnified real image. What is focal length of the concave mirror ?
We know that
Linear magnification $m=\frac{f}{f-u}$
Given, object displaced $u=-20 \,cm$
$m=-3$
$(\because$ all real image are inverted)
So, $-3=\frac{f}{f-(-20)}$
$-3=\frac{f}{f+20}$
$ \Rightarrow -3 f-60=f$
$4 f=-60$
$\Rightarrow f=-\frac{60}{4}=-15 cm$
Since, mirror is concave $f=-15 \,cm$.