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 $\sqrt{5} = 2.3$)

$A$ ray of light making an angle $10^o$ with the horizontal is incident on a plane mirror making an angle $\theta$ with the horizontal. What should be the value of $\theta$ so that the reflected ray goes vertically upwards?

$A$ beam of light from a source $L$ is incident normally on a plane mirror fixed at a certain distance $x$ from the source. The beam is reflected back as a spot on a scale placed just above the source $L$. When the mirror is rotated through a small angle $\theta$,the spot of the light is found to move through a distance $y$ on the scale. The angle $\theta$ is given by

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 ......$^{\circ}$.

$A$ point object is placed mid-way between two plane mirrors at a distance $a$ apart. The plane mirrors form an infinite number of images due to multiple reflections. The distance between the $n^{th}$ order images formed in the two mirrors is

$A$ 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 $(3,3)$?