The figure shows two rays $A$ and $B$ being reflected by a mirror and emerging as $A'$ and $B'$. The mirror

$A$ man of height $170 \, cm$ wants to see his complete image in a plane mirror (while standing). His eyes are at a height of $160 \, cm$ from the ground. Which of the following statements are correct?
$(a)$ Minimum length of mirror is $80 \, cm$
$(b)$ Minimum length of mirror is $85 \, cm$
$(c)$ Bottom of the mirror should be at a height $80 \, cm$
$(d)$ Bottom of the mirror should be at a height $85 \, cm$

Each of these diagrams is supposed to show two different rays being reflected from the same point on the same plane mirror. Which one of the following is correct?

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

For a plane mirror,the focal length is . . . . . . $m$.

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