$A$ 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 $cm$?

$A$ long horizontal mirror is next to a vertical screen (see figure). Parallel light rays are falling on the mirror at an angle $\alpha$ from the vertical. If a vertical object of height $h$ is kept on the mirror at a distance $d$ from the screen,where $d > h \tan \alpha$,the length of the shadow of the object on the screen would be

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?

Two plane mirrors $A$ and $B$ are placed parallel to each other as shown in the figure. $A$ light ray is incident on mirror $A$ at an angle of $30^o$. The plane of incidence coincides with the plane of the figure. What is the maximum number of reflections (including the first one) the ray will undergo before emerging?

$A$ plane mirror produces a magnification of

What should be the angle between two plane mirrors so that whatever be the angle of incidence,the incident ray and the reflected ray from the two mirrors are parallel to each other (in $^o$)?