Question

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:

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

Answer 1

The correct option is D $36cm$ away from the mirror

Initially:

$u_i=-40$cm $f_i=-15$cm

$\frac{1}{v_i}+\frac{1}{u_i}=\frac{1}{f}$

$\frac{1}{v_i}+\frac{1}{-40}=\frac{1}{-15}$ $\Rightarrow v_i=-24$cm

Finally: $u_f=-20cm$ $f=-15$cm

$\frac{1}{v_f}+\frac{1}{u_f}=\frac{1}{f}$

$\therefore \frac{1}{v_f}+\frac{1}{-20}=\frac{1}{-15}$ $\Rightarrow v_f=-60$cm

Thus image is shifted by $60-24=36$cm

(away from mirror)

Option (4) is correct.