An object is placed at a distance of $40 \mathrm{~cm}$ from a concave mirror of focal length $15 \mathrm{~cm}$. If the object is displaced through a distance of $20 \mathrm{~cm}$ towards the mirror, the displacement of the image will be
(1) $30 \mathrm{~cm}$ towards the mirror
(2) $36 \mathrm{~cm}$ away from the mirror
(3) $30 \mathrm{~cm}$ away from the mirror
(4) $36 \mathrm{~cm}$ towards the mirror
An object is placed at a distance of $40 \mathrm{~cm}$ from a concave mirror of focal length $15 \mathrm{~cm}$. If the object is displaced through a distance of $20 \mathrm{~cm}$ towards the mirror, the displacement of the image will be
(1) $30 \mathrm{~cm}$ towards the mirror
(2) $36 \mathrm{~cm}$ away from the mirror
(3) $30 \mathrm{~cm}$ away from the mirror
(4) $36 \mathrm{~cm}$ towards the mirror

$\frac{1}{f}=\frac{1}{v_{1}}+\frac{1}{u}$

$-\frac{1}{15}=\frac{1}{v_{1}}-\frac{1}{40}$

$\Rightarrow \frac{1}{v_{1}}=\frac{1}{-15}+\frac{1}{40}$

$v_{1}=-24 \mathrm{~cm}$

Now object is displaced by $20 \mathrm{~cm}$ towards mirror.

So,

$\mathrm{u}_{2}=-20$

$\frac{1}{f}=\frac{1}{v_{2}}+\frac{1}{u_{2}}$

$\frac{1}{-15}=\frac{1}{v_{2}}-\frac{1}{20}$

$\frac{1}{v_{2}}=\frac{1}{20}-\frac{1}{15}$

$\mathrm{v}_{2}=-60 \mathrm{~cm}$

So, image shifts away from mirror by $=60-24=36 \mathrm{~cm}$