$A$ 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 ...... $cm/s$.

$A$ ray of light travelling in the direction $\frac{1}{2}(\hat{i}+\sqrt{3} \hat{j})$ is incident on a plane mirror. After reflection,it travels along the direction $\frac{1}{2}(\hat{i}-\sqrt{3} \hat{j})$. The angle of incidence is: (in $^{\circ}$)

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 reflecting surface of a plane mirror is vertical. $A$ particle is projected in a vertical plane which is also perpendicular to the mirror. The initial velocity of the particle is $10 \, m/s$ and the angle of projection is $60^\circ$ with the horizontal. The point of projection is at a distance $5 \, m$ from the mirror. The particle moves towards the mirror. Just before the particle touches the mirror,the velocity of approach of the particle and its image is ...... $m/s$.

$A$ 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 at $70^{\circ}$. $A$ ray incident on one mirror at an angle $\theta$ with the surface,after reflection,falls on the second mirror and is reflected from there parallel to the first mirror. The value of $\theta$ is ......$^{\circ}$.