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. 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} = - 24 \,cm $
When object is displaced by $20 \,cm$ 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} = - 60 \,cm $
So, image shifts away from mirror by $= 60 - 24 = 36\, cm.$