A diverging lens of focal length –10 cm is moving towards right with a velocity 5 m/s. An object, placed on Principal axis is moving towards left with a velocity 3 m/s. Find the velocity of image at the instant when the lateral magnification produced is 1/2. All velocities are with respect to ground.

7 m/s towards right

$\frac{dv}{dt}=\frac{v^2}{\mathrm{u}^2} . \frac{du}{dt}$

(where $\frac{dv}{dt}$ denotes image speed w.r.t. lens and $\frac{du}{dt}$ denotes object speed w.r.t. lens)

$=m^2 . \frac{du}{dt}=\frac{1}{4} . 8=2$

Therefore image speed w.r.t. lens is 2 m/s

Therefore image speed w.r.t. ground is 7 m/s towards right.