Two plane mirrors are kept at an angle $\theta$ such that the emergent ray (after second reflection) is always antiparallel to incident ray for any angle of incidence. Find the value of $\theta$.

Two plane mirrors are kept on a horizontal table making an angle $\theta$ with each other as shown schematically in the figure. The angle $\theta$ is such that any ray of light reflected after striking both the mirrors return parallel to its incident path. For this to happen, the value of $\theta$ should be

Letters $A,B,C$ and $D$ are written on a cardboard as shown in the figure below.

The cardboard is kept at a suitable distance behind a transparent empty glass of cylindrical shape. If the glass is now filled with water, one sees an inverted image of the pattern on the cardboard when looking through the glass. Ignoring magnification effects, the image would appear as

The image of an object $O$ due to reflection from the surface of a lake is elongated due to the ripples on the water surface caused by a light breeze. This is because the ripples act as tilted mirrors as shown below. Consider the case, where $O$ and the observer $E$ are at the same height above the surface of the lake. If the maximum angle that the ripples make with the horizontal is $\alpha$, then the angular extent $\delta$ of the image will be

A mirror is placed at an angled of $30°$ with respect to $y-$axis (see figure). A light ray travelling in the negative $y-$direction strikes the mirror. The direction of the reflected ray is given by the vector

A point source of light $S$, placed at a distance $60 \mathrm{cm}$ infront of the centre of a plane mirror of width $50 \mathrm{cm}$, hangs vertically on a wall. A man walks infront of the mirror along a line parallel to the mirror at a distance $1.2 \mathrm{m}$ from it (see in the figure). The distance between the extreme points where he can see the image of the light source in the mirror is__$\mathrm{cm}$

A point source of light, $S$ is placed at a distance $L$ in front of the center of plane mirror of width $d$ which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance $2L$ as shown below. The distance over which the man can see the image of the light source in the mirror is:

A ray of light is reflected by a plane mirror. ${\hat{e}}_0, \hat{e}$ and $\hat{n}$ be the unit vectors along the incident ray, reflected ray and the normal to the reflecting surface respectively. Which of the following gives an expression for $\hat{e}?$

A monochromatic beam of light enters a square enclosure with mirrored interior surfaces at an angle of incidence ${\theta }_i=(\ne 0)$ (see the figure below). For some value(s) of ${\theta }_i$, the beam is reflected by every mirrored wall (other than the one with opening) exactly once and exists the enclosure through the same hole. Which of the following statements about this beam is correct?