Question

An object is moving towards a concave mirror of focal length 24 cm. When it is at a distance of 60 cm from the mirror its speed is 9cm/s, the speed of its image at that instant is :

• A. 4 cm/s towards the mirror
• B. 9 cm/s towards the mirror
• C. 4 cm/s away from the mirror
• D. 9 cm/s away from the mirror

Answer 1

Answer: (C)

4 cm/s away from the mirror

For a concave mirror, we use the mirror formula
$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$

Now, given$u$=$-60cm,f$=$-24cm$

Putting the values in the expression,

$\frac{1}{v}=\frac{-1}{24}+\frac{1}{60}$

This gives, $v=-40cm$

Now, for relating the velocities, we differentiate the mirror formula,to obtain,

$\frac{-u^{\prime }}{u^2}-\frac{-v^{\prime }}{v^2}=$ 0

Now, $u^{\prime }=9cm/s$

Substituting these values, we get

$\frac{9}{3600}=-\frac{v^{\prime }}{1600}$

$v^{\prime }=-4cm/s$