A point object $O$ is moving with a velocity of $v$ in front of an arrangement of plane mirrors as shown in the figure. The magnitude of velocity of image in mirror $M_1$ with respect to the image in mirror $M_2$ will be

1. $2v\sin \theta$
2. $2v\cos \theta$
3. $3v\cos \theta$
4. $3v\sin \theta$

The correct option is A $2v\sin \theta$
We know that for the fixed plane mirror,
$\left(1\right)$ Along perpendicular to the mirror, $v_o=-v_i$
$\left(2\right)$ Along parallel to the mirror, $v_o=v_i$

The image velocity for both mirrors are shown below,


Resolving components of velocity of image $2$ along and perpendicular to mirror $M_1$,


Thus, the velocity of image $1$ $w.r.t$ to image $2$ will be,


Magnitude of velocity of image $1$ in mirror $M_1$ $w.r.t$ image $2$ in mirror $M_2$,
$|{\overrightarrow{v}}_{12}|=2v\sin \theta$