$A$ long horizontal mirror is next to a vertical screen (see figure). Parallel light rays are falling on the mirror at an angle $\alpha$ from the vertical. If a vertical object of height $h$ is kept on the mirror at a distance $d$ from the screen,where $d > h \tan \alpha$,the length of the shadow of the object on the screen would be

$A$ 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 $85 \, cm$

Two plane mirrors $A$ and $B$ are aligned parallel to each other,as shown in the figure. $A$ light ray is incident at an angle of $30^\circ$ at a point just inside one end of $A$. The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is

$A$ 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 $cm$)

$A$ ray of light travelling in the direction $\frac{1}{2}(\hat{i}+\sqrt{3} \hat{j})$ is incident on a plane mirror. After reflection,it travels along the direction $\frac{1}{2}(\hat{i}-\sqrt{3} \hat{j})$. The angle of incidence is: (in $^{\circ}$)

$A$ 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?