Question

An object is $20\text{cm}$ away from a stationary concave mirror having focal length $15\text{cm}$. If the object moves with a speed of $5\text{m/s}$ along the principal axis towards the mirror, then the speed of the image will be

Answer 1

For the given concave mirror,
$u=-20\text{cm},f=-15\text{cm}$
Using mirror formula,
$\frac{1}{v}-\frac{1}{20}=\frac{-1}{15}$
$\Rightarrow \frac{1}{v}=\frac{-1}{60}$
$\Rightarrow v=-60\text{cm}$
So, $m=\frac{-v}{u}=\frac{-(-60)}{-20}=-3$
Also, velocity of the image when the object is moving along the principal axis,
$v_{i,m}=-m^2{v}_{o,m}$
$\Rightarrow v_{i,m}=-(-3{)}^2\times 5=-45\text{m/s}$
Hence, the speed of the image will be $45\text{m/s}$.
$\begin{array}{c}\text{Why this question?}\\ \text{Caution: While applying formula of magnification and image velocity, always}\\ \text{take care of sign convention.}\\ \end{array}$