Question

A luminous point object is moving along the principal axis of a concave mirror of focal length $12cm$ towards it. When its distance from mirror is $20cm$ its velocity is $4cm/s$. The velocity of the image in $cm/s$ at that instant is :

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

Answer 1

Answer: (C)

Using mirror formula
$v=+30cm$ as $f=12u=-20$
Now, $\frac{du}{dt}\left(\frac{-1}{u^2}\right)=\frac{1}{v^2}\left(\frac{dv}{dt}\right)$
$\frac{du}{dt}=-4$ (towards mirror so -ve)
$\therefore \frac{4}{20^2}=\frac{1}{30^2}\times \frac{dv}{dt}$
So $\frac{dv}{dt}=9cm/s$
+ve so away from the mirror.