If $\hat{n}_1, \hat{n}_2$ and $\hat{t}$ represent unit vectors along the incident ray,reflected ray,and normal to the surface respectively,then:

$A$ ray of light is incident at $50^{\circ}$ on the middle of one of the two mirrors arranged at an angle of $60^{\circ}$ between them. The ray then touches the second mirror,gets reflected back to the first mirror,making an angle of incidence of.........$^{\circ}$

Two plane mirrors $M_1$ and $M_2$ have a length of $20 \, m$ each and are $10 \, cm$ apart. $A$ ray of light is incident on one end of mirror $M_2$ at an angle of $53^{\circ}$. The number of reflections the light undergoes before reaching the other end is

$A$ point source of light $S$ is placed at a distance $10\,cm$ in front of the centre of a mirror of width $20\,cm$ suspended vertically on a wall. $A$ man walks with a speed $10\,cm/s$ in front of the mirror along a line parallel to the mirror at a distance $20\,cm$ from it as shown in the figure. Find the maximum time during which he can see the image of the source $S$ in the mirror. (in $,s$)

$A$ man $160\,cm$ high stands in front of a plane mirror. His eyes are at a height of $150\,cm$ from the floor. The minimum length of the plane mirror required for him to see his full-length image is......$cm$.

An object $O$ is placed between two parallel plane mirrors $M_1$ and $M_2$. The distance of the object from $M_1$ is $6\,cm$ and from $M_2$ is $15\,cm$. The position of the $4^{th}$ image formed by mirror $M_1$ is: