It is necessary to illuminate the bottom of a well by reflected solar beam when the light is incident at an angle of $\mathrm{\alpha }=40°\mathrm{ }$to the vertical. At what angle $\mathrm{\beta }\mathrm{ }$to the horizontal should a plane mirror be placed?

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

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 light ray is incident, at an incident angle ${\theta }_1$, on the system of two plane mirrors $M_1$ and $M_2$ having an inclination angle $75°$ between them (as shown in figure). After reflecting from mirror $M_1$ it gets reflected back by the mirror $M_2$ with an angle of reflection $30°$. The total deviation of the ray will be _____ degree.

Three plane mirrors form an equilateral triangle with each side of length $L$. There is a small hole at a distance $l>0$ from one of the corners as shown in the figure. A ray of light is passed through the hole at an angle $\theta$ and can only come out through the same hole. The cross section of the mirror configuration and the ray of light lie on the same plane.

Which of the following statement(s) is(are) correct?

Image formed by a plane mirror is erect, virtual and _____.

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

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: