An object is placed at a distance of 40cm from a concave mirror of focal length 15cm. If the object is displaced through a distance of 20cm towards the mirror, the displacement of the image will be

Using mirror formula,

$\begin{array}{l}\frac{1}{f}=\frac{1}{v_1}+\frac{1}{u};-\frac{1}{15}=\frac{1}{v_1}-\frac{1}{40}\Rightarrow \frac{1}{v_1}=\frac{1}{-15}+\frac{1}{40}\\ v_1=-24 \mathrm{cm}\end{array}$

When object is displaced by 20 cm  towards mirror. 

Now,$u_2=-20 \mathrm{cm}$

$\begin{array}{l}\frac{1}{f}=\frac{1}{v_2}+\frac{1}{u_2};\frac{1}{-15}=\frac{1}{v_2}-\frac{1}{20}\Rightarrow \frac{1}{v_2}=\frac{1}{20}-\frac{1}{15}\\ v_2=-60 \mathrm{cm}\end{array}$

So, the image will shift away from mirror by (60-24)cm=36 cm