Question

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

• A. $0.4cm$ away from the mirror
• B. $0.4cm$ towards the mirror
• C. $0.8cm$ away from the mirror
• D. $0.8cm$ 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 $0.1cm$ then.
$u=(10-0.1)=9.9cm$.
Hence again from mirror formula $\frac{1}{-20/3}=\frac{1}{v^{\prime }}=\frac{1}{-9.9}$
$\Rightarrow v^{\prime }=20.4cm$
i.e.,image shifts away from the mirror by $0.4cm$.