Question

Using a certain concave mirror, the magnification is found to be $4$ times as great when the object was $25 \,cm$ from the mirror as it was with the object at $40\, cm$ from the mirror, the image being real in each case. The focal length of the mirror (in $cm$ ) is________.

Answer 1

We use magnification, $m=\frac{v}{u}=\frac{f}{u-f}$
In first case when $u=25 \,cm$, magnification is
$m_{1}=\frac{f}{25-f}$......(i)
In second case when $u=40 \,cm$, magnification is
$m_{2}=\frac{f}{40-f}$......(ii)
As it is given that $m_{1}=4 m_{2}$,
we use $\frac{f}{25-f}=4\left(\frac{f}{40-f}\right)$
Solving we get $f=20 \,cm$.