Question

An object is kept on the principal axis of a convex mirror of focal length $10\text{cm}$ at a distance of $10\text{cm}$ from the pole. The object starts moving at a velocity $20\text{mm/sec}$ towards the mirror at angle ${30}^o$ with the principal axis. What will be the speed of its image

Answer 1

By the mirror formula ,

$\frac{1}{v}=\frac{1}{f}-\frac{1}{u}=\frac{1}{+10}-\frac{1}{-10}$

$\Rightarrow v=\frac{10}{2}=5\text{cm}$

$V_{I_x}=-\frac{(5{)}^2}{(-10{)}^2}(20\times \frac{\sqrt{3}}{2})=\frac{-5\sqrt{3}}{2}\text{mm/s}$

$V_{I_y}=-\frac{5}{(-10)}\times 20\times \frac{1}{2}==5\text{mm//s}$

Speed of image $V=\sqrt{{(-\frac{5\sqrt{3}}{2})}^2+{\left(5\right)}^2}=\frac{5\sqrt{7}}{2}\text{mm/s}$

Hence, option (b) is the correct answer.