$A$ man is $180\,cm$ tall and his eyes are $10\,cm$ below the top of his head. In order to see his entire height from toe to head,he uses a plane mirror kept at a distance of $1\,m$ from him. The minimum length of the plane mirror required is.....$cm$.

The figure shows a cubical room $ABCD$ with the wall $CD$ as a plane mirror. Each side of the room is $3\,m$. $A$ camera is placed at the midpoint of the wall $AB$. At what distance should the camera be focused to photograph an object placed at $A$?

$A$ plane mirror makes an angle of $30^\circ$ with the horizontal. If a vertical ray strikes the mirror,find the angle between the mirror and the reflected ray.

Two plane mirrors are inclined to one another at an angle of $60^o$. $A$ ray is incident on mirror $M_1$ at an angle $i$. The reflected ray from mirror $M_1$ is shown in the figure. The angle of incidence $i$ is (in $^o$)

$A$ point source is placed at coordinates $(0,1)$ in the $xy$-plane. $A$ ray of light from the source is reflected on a plane mirror placed along the $X$-axis and perpendicular to the $xy$-plane. The reflected ray passes through the point $(3,3)$. What is the path length of the ray from $(0,1)$ to $(3,3)$?

Two plane mirrors ${M}_{1}$ and ${M}_{2}$ are at a right angle to each other as shown. $A$ point source $P$ is placed at distances of $a$ and $2a$ meters from ${M}_{1}$ and ${M}_{2}$ respectively. The longest distance between the images thus formed is: (Take $\sqrt{5} = 2.3$)