Question

What is the velocity (in cm/s) of image in situation shown below. ($O=object,f=focallength)$. Object moves with velocity $10cm/s$ and mirror moves with velocity $2cm/s$ as shown.

Answer 1

Let us first find the position of the image .
$\frac{1}{v}+\frac{1}{u}$ = $\frac{1}{f}$
$\frac{1}{v}+\frac{1}{-10}$ = $\frac{1}{10}$
$v=5cm.$
Let the velocity of the image be V towards the right .
With respect to the mirror , image will have a velocity of $V-2$ and the object will have a velocity of $10-2=8$
On differentiating the mirror equation , we get
$\frac{-V}{v^2}+\frac{-U}{u^2}$ = 0
$\frac{-(V-2)}{5^2}+\frac{-8}{{10}^2}$ = 0
$V=2+\frac{-8\times 5^2}{{10}^2}$
$\therefore$ V = 0