Question

A point object is moving towards a concave mirror of focal length $12\text{cm}$ along its principal axis. When its distance from the mirror is $20\text{cm}$, its velocity is $4\text{cm/s}$. Then the velocity of the image at this instant will be

• A. $9\text{cm/s}$ towards the mirror
• B. $9\text{cm/s}$ away from the mirror
• C. $6\text{cm/s}$ away from the mirror
• D. $6\text{cm/s}$ towards the mirror

Answer 1

The correct option is B $9\text{cm/s}$ away from the mirror

For the given concave mirror,
$u=-20\text{cm},f=-12\text{cm}$

Using mirror formula,
$\frac{1}{v}-\frac{1}{20}=\frac{-1}{12}$
$\Rightarrow \frac{1}{v}=\frac{-1}{30}$
$\Rightarrow v=-30\text{cm}$

So, $m=\frac{-v}{u}=\frac{-(-30)}{-20}=\frac{-3}{2}$

Also, velocity of the image when the object is moving along the principal axis,
$v_i=-m^2{v}_o$

$\Rightarrow v_i=-{\left(\frac{-3}{2}\right)}^2\times 4=-9\text{cm/s}$
Here the $-ve$ sign indicates that the image is moving in the direction opposite to incident ray hence the velocity of the image will be $9\text{cm/s}$ away from the mirror.

Why this question? To boost practice of sign convention in problems of image velocity.