A child is standing in front of a straight plane mirror. His father is standing behind him, as shown in the figure. The height of the father is double the height of the child. What is the minimum length of the mirror required so that the child can completely see his own image and his father's image in the mirror? Given the height of the father is $2H$.

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Two vertical parallel mirrors $\mathrm{A}$ and $\mathrm{B}$ are separated by $10$ cm. $\mathrm{A}$ point object $\mathrm{O}$ is placed at a distance of $2 \mathrm{cm}$ from mirror $\mathrm{A}.$ The distance of the second nearest image behind mirror $\mathrm{A}$ from the mirror $\mathrm{A}$ is $\_\_\_\_\_\_\_ \mathrm{cm}.$

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

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 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.

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 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: