Question

An object is moving towards a stationary concave mirror of focal length $24\text{cm}$. When it is at a distance of $60\text{cm}$ from the mirror, its speed is $9\text{cm/s}$. The velocity of its image at this instant will be

• A. $4\text{cm/s}$ towards the mirror
• B. $6\text{cm/s}$ towards the mirror
• C. $4\text{cm/s}$ away from the mirror
• D. $6\text{cm/s}$ away from the mirror

Answer 1

The correct option is C $4\text{cm/s}$ away from the mirror

For the given concave mirror,
$u=-60\text{cm},f=-24\text{cm}$
Using mirror formula,
$\frac{1}{v}-\frac{1}{60}=\frac{-1}{24}$
$\Rightarrow \frac{1}{v}=\frac{-1}{40}$
$\Rightarrow v=-40\text{cm}$
So, $m=\frac{-v}{u}=\frac{-(-40)}{-60}=\frac{-2}{3}$
Also, velocity of the image when the object is moving along the principal axis,
$v_{i,m}=-m^2{v}_{o,m}$
$\Rightarrow v_{i,m}=-{\left(\frac{-2}{3}\right)}^2\times 9=-4\text{cm/s}$
Hence, the velocity of the image will be $4\text{cm/s}$ away from the mirror.
$\begin{array}{c}\text{Why this question?}\\ \text{Tips: Always read the questions carefully, as it reveals}\\ \text{the intent of question. The direction of object motion}\\ \text{is giving the hint to use formula with sign convention.}\end{array}$