$A$ 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:

An object is at a distance of $0.5 \ m$ in front of a plane mirror. The distance between the object and its image is ..... $m$.

The incident ray,reflected ray,and the outward drawn normal are denoted by the unit vectors $\overrightarrow{ a }, \overrightarrow{ b }$ and $\overrightarrow{ c }$ respectively. Choose the correct relation for these vectors.

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 $\sqrt{5} = 2.3$)

$A$ man runs towards a plane mirror at a speed of $15 \, m/s$. The speed of the image relative to the mirror is ...... $m/s$.

By what angle should $M_2$ be rotated,so that the light ray after reflection from both mirrors becomes horizontal? (The angle of incidence at mirror $M_1$ is $40^{\circ}$ and the angle between $M_2$ and the horizontal is $25^{\circ}$ as shown in the figure.)