When one light ray is reflected from a plane mirror with $30^{\circ}$ angle of reflection,the angle of deviation of the ray after reflection is $.....^{\circ}$

$A$ cubical room is made of mirrors. An insect is moving along the diagonal on the floor such that the velocity of the image of the insect on two adjacent wall mirrors is $10 \, cm \, s^{-1}$. The velocity of the image of the insect in the ceiling mirror is:

$A$ 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?

Power of a plane mirror is . . . . . .

$A$ 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 $85 \, cm$