$A$ man moves towards a plane mirror with a velocity $v$ in a direction making an angle $\theta$ with the normal to the mirror. The magnitude of the velocity of the image relative to the man is:

$A$ man has a height of $180\, cm$ and his eyes are $10\, cm$ below the top of his head. He uses a plane mirror placed $1\, m$ away to see his full height from head to toe. What is the minimum required height of the plane mirror in $cm$?

An object is fixed at the bottom of a vessel and water is filled in the vessel up to a height of $10 \,cm$. $A$ plane mirror is placed at a height of $7 \,cm$ from the surface of water in such a way that its reflecting surface faces the water. The distance of the image from the mirror is (Refractive index of water,$n=1.33$). (in $\,cm$)

$A$ point source of light $S$ at a distance $d$ from the screen $A$ produces light intensity $I_0$ at the centre of the screen. If a completely reflecting mirror $M$ is placed at a distance $d$ behind the source as shown in the figure,treating the object and its image as incoherent with each other,find the intensity at the centre of the screen.

Two plane mirrors are at right angles to each other. $A$ man stands between them and combs his hair with his right hand. In how many of the images will he be seen using his right hand?

$A$ point source of light $B$ is placed at a distance $L$ in front of the centre of a mirror of width $d$ hung vertically on a wall. $A$ man walks in front of the mirror along a line parallel to the mirror at a distance $2L$ from it as shown. The greatest distance over which he can see the image of the light source in the mirror is