If $\hat{n}_1, \hat{n}_2$ and $\hat{t}$ represent unit vectors along the incident ray, reflected ray, and normal to the surface respectively, then:

$A$ girl of height $150 \,cm$ with her eye level at $140 \,cm$ stands in front of a plane mirror of height $75 \,cm$ fixed to a wall. The lower edge of the mirror is at a height of $85 \,cm$ above her feet level. The height of her image the girl can see in the mirror is (in $cm$)

$A$ small plane mirror is placed at the centre of a spherical screen of radius $R$. $A$ beam of light is falling on the mirror. If the mirror makes $n$ revolutions per second,the speed of the reflected light spot on the screen will be:

$A$ 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

$A$ 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........$cm$.

$A$ laser beam is incident on a plane mirror at some angle and results in a reflected beam. The mirror is now rotated by an angle $\delta$ while the direction of the incident laser beam is kept the same. The angle between the new reflected beam and the reflected beam before the mirror was rotated is