$A$ light ray makes an angle of $10^{\circ}$ with the horizontal. It is incident on a plane mirror which makes an angle $\theta$ with the horizontal. If the reflected ray travels in the vertically upward direction,then $\theta = .....^{\circ}$

$A$ 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

Find the angle of deviation for the given diagram.

$A$ plane mirror makes an angle of $30^\circ$ with the horizontal. $A$ vertical ray is incident on the mirror. What is the angle between the mirror and the reflected ray in degrees?

$A$ 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:

$A$ cubical room is formed with $6$ plane mirrors. An insect moves along the diagonal of the floor with uniform speed $v_0$. The speed of its image in two adjacent walls,parallel to the walls,is $20\sqrt{2} \ cm/s$. Then the speed of the image formed on the roof with respect to the ground is ...... $cm/s$.