$A$ 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 $cm$?

$A$ person runs with a speed $u$ towards a bicycle moving away from him with speed $v$. The person approaches his image in the mirror fixed at the rear of the bicycle with a speed 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 $^o$)?

When a plane mirror is rotated through an angle $\theta$,the reflected ray turns through an angle $2\theta$. What happens to the size of the image?

The image of an object $O$ due to reflection from the surface of a lake is elongated due to the ripples on the water surface caused by a light breeze. This is because the ripples act as tilted mirrors as shown below. Consider the case,where $O$ and the observer $E$ are at the same height above the surface of the lake. If the maximum angle that the ripples make with the horizontal is $\alpha$,then the angular extent $\delta$ of the image will be

Digital movie projectors work on the principle of