Question

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

• A. 30 cm away from the mirror
• B. 36 cm away from the mirror
• C. 36 cm towards the mirror
• D. 30 cm towards the mirror

Answer 1

The correct option is B 36 cm away from the mirror

$\begin{array}{c}\text{Using mirror formula.}\\ \therefore \frac{1}{f}=\frac{1}{v_1}+\frac{1}{u_1}(u_1=-40cm)\\ \therefore \frac{1}{-15}=\frac{1}{v_1}-\frac{1}{40}\\ \therefore v_1=\frac{-40+15}{-40+15}\\ \therefore v_1=-24cm\end{array}$

When object is placed $20cm$ towards the mirro?

$\begin{array}{cc}{u}_2& =-20cm\\ \frac{1}{f}& =\frac{1}{v_2}+\frac{1}{u_2}\\ \Rightarrow & \frac{1}{-15}=\frac{1}{v_2}-\frac{1}{20}\\ & \Rightarrow v_2=\frac{-15-20}{-20+15}\\ & \Rightarrow v_2=-60cm\end{array}$

So, the image will be shift away from mirror

$\begin{array}{cc}& \left|v_2\right|\left|v_1\right|\\ \therefore & 60-24\end{array}$

$\therefore 36cm$ away from the mirror

Hence, $\left(B\right)$ is correct option