$A$ tall man of height $6$ feet wants to see his full image. The required minimum length of the mirror will be ......... feet.

$A$ point object is kept in front of a plane mirror. The plane mirror is performing $SHM$ with an amplitude of $2 \ cm$. The plane mirror moves along the $x$-axis,and the $x$-axis is normal to the mirror. The amplitude of the mirror is such that the object is always in front of the mirror. The amplitude of the $SHM$ of the image is ....... $cm$.

$A$ small object is placed $10\, cm$ in front of a plane mirror. If you stand behind the object $30\, cm$ from the mirror and look at its image,the distance focused for your eye will be........$cm$.

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

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

$A$ ray of light is incident on a plane mirror at rest. The mirror starts turning at a uniform angular acceleration of $4\pi \, rad/s^2$. The reflected ray at the end of $\frac{1}{4} \, s$ must have turned through......$^o$