$A$ plane mirror is placed along the $x$-axis facing the negative $y$-axis. The mirror is fixed. $A$ point object is moving with a velocity of $3\hat{i} + 4\hat{j}$ in front of the plane mirror. Find the relative velocity of the image with respect to the object.

An object is at a distance of $20\,m$ from a convex lens of focal length $0.3\,m$. The lens forms an image of the object. If the object moves away from the lens at a speed of $5\,m/s$,the speed and direction of the image will be

$A$ point object is moving uniformly towards the pole of a concave mirror of focal length $25 \ cm$ along its axis as shown below. The speed of the object is $1 \ ms^{-1}$. At $t=0$,the distance of the object from the mirror is $50 \ cm$. The average velocity of the image formed by the mirror between time $t=0$ and $t=0.25 \ s$ is

$A$ point object is kept in front of a plane mirror. The plane mirror is performing $SHM$ with an amplitude of $2 \ cm$. The plane mirror moves along the $x-$ axis,which is normal to the mirror. The amplitude of the mirror is such that the object is always in front of the mirror. The amplitude of the $SHM$ of the image is .... $cm$.

$A$ point object is moving on the principal axis of a concave mirror of focal length $24\;cm$,towards the mirror. When it is at a distance of $60\;cm$ from the mirror,its velocity is $9\;cm/sec$. What is the velocity of the image at that instant?

An object is moving in front of a mirror as shown in the figure. Match the items in Column-$I$ with the values in Column-$II$.

$(i)$ Velocity of image	$(a) \; 2 \; m/s$
$(ii)$ Velocity of image with respect to mirror	$(b) \; 20 \; m/s$
$(iii)$ Velocity of image with respect to object	$(c) \; 11 \; m/s$
$(iv)$ Velocity of image if mirror is stopped	$(d) \; 22 \; m/s$