$A$ small plane mirror is placed at the centre of a spherical screen of radius $R$. $A$ beam of light is falling on the mirror. If the mirror makes $n$ revolutions per second,the speed of the reflected light spot on the screen will be:

Two plane mirrors are kept on a horizontal table making an angle $\theta$ with each other as shown schematically in the figure. The angle $\theta$ is such that any ray of light reflected after striking both the mirrors returns parallel to its incident path. For this to happen,the value of $\theta$ should be (in $^{\circ}$)

Digital movie projectors work on the principle of

Two plane mirrors are inclined at $70^{\circ}$. $A$ ray incident on one mirror at an angle $\theta$ with the surface,after reflection,falls on the second mirror and is reflected from there parallel to the first mirror. The value of $\theta$ is ......$^{\circ}$.

Each of these diagrams is supposed to show two different rays being reflected from the same point on the same plane mirror. Which one of the following is correct?

$A$ 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 $cm$?