Question

A point object is placed at a distance of $10\,cm$ and its real image is formed at a distance of $20 \,cm$ from a concave mirror. If the object is moved by $0.1 \,cm$ towards the mirror, the image will shift by about

• A. $0.4 \,cm$ away from the mirror
• B. $0.4\,cm$ towards the mirror
• C. $0.8 \,cm$ away from the mirror
• D. $0.8 \,cm$ towards the mirror

Answer 1

Answer: (A)

Mirror formula
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u} \Rightarrow \frac{1}{f}=\frac{1}{-20}+\frac{1}{(-10)}$
$ \Rightarrow f=\frac{20}{3} cm .$ If
object moves towards the mirror by $0.1 \,cm$ then.
$u=(10-0.1)=9.9 \,cm$.
Hence again from mirror formula $\frac{1}{-20 / 3}=\frac{1}{v^{\prime}}=\frac{1}{-9.9} $
$\Rightarrow v^{\prime}=20.4 \,cm$
i.e.,image shifts away from the mirror by $0.4\, cm$.