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

Answer 1

Answer: (D)

$\frac{1}{f}=\frac{1}{v_1}+\frac{1}{u}$
$-\frac{1}{15}=\frac{1}{v_1}-\frac{1}{40}$
$\Rightarrow \frac{1}{v_1}=\frac{1}{-15}+\frac{1}{40}$
$v_1=-24cm$
When object is displaced by $20cm$ towards mirror.
Now,
$u_2=-20$
$\frac{1}{f}=\frac{1}{v_2}+\frac{1}{u_2}$
$\frac{1}{-15}=\frac{1}{v_2}-\frac{1}{20}$
$\frac{1}{v_2}=\frac{1}{20}-\frac{1}{15}$
$v_2=-60cm$
So, image shifts away from mirror by $=60-24=36cm.$