Question

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. The velocity of the image at the instant when the lateral magnification produced is $1/2$ is: (All velocities are with respect to ground)

• A. $3$ m/s towards right
• B. $3$ m/s towards left
• C. $7$ m/s towards right
• D. $7$ m/s towards left

Answer 1

The correct option is A $3$ m/s towards right

$\begin{array}{c}f=-10cm\\ M=\frac{1}{2}=\left(\frac{v}{u}\right)\\ v_{IM}=\left(\frac{v^2}{u^2}\right)v_{OM}\\ \Rightarrow v_I-v_M=\frac{1}{4}\left(v_O-v_M\right)\\ v_I-5=\frac{1}{4}\left[-3-5\right]\\ v_I-5=-2\\ v_I=3m/stowardsright\end{array}$

Hence,

option $\left(A\right)$ is correct answer.