In the figure shown,consider the first reflection at the plane mirror and the second at the convex mirror. $AB$ is the object.

Three plane mirrors form an equilateral triangle with each side of length $L$. There is a small hole at a distance $l > 0$ from one of the corners as shown in the figure. $A$ ray of light is passed through the hole at an angle $\theta$ and can only come out through the same hole. The cross section of the mirror configuration and the ray of light lie on the same plane.
Which of the following statement(s) is(are) correct?
$(A)$ The ray of light will come out for $\theta=30^{\circ}$, for $0 < l < L$.
$(B)$ There is an angle for $l=\frac{L}{2}$ at which the ray of light will come out after two reflections.
$(C)$ The ray of light will $NEVER$ come out for $\theta=60^{\circ}$, and $l=\frac{L}{3}$.
$(D)$ The ray of light will come out for $\theta=60^{\circ}$, and $0 < l < \frac{L}{2}$ after six reflections.

$A$ luminous object is placed $20 \, cm$ from the surface of a convex mirror and a plane mirror is adjusted in such a way that the virtual images formed by the two mirrors coincide. If the focal length of the convex mirror is $5 \, cm$,then the distance between the plane mirror and the object will be......$cm$.

Two plane mirrors of length $L$ are separated by a distance $L$,and a man $M_2$ is standing at a distance $L$ from the connecting line of the mirrors,as shown in the figure. $A$ man $M_1$ is walking in a straight line at a distance $2L$ parallel to the mirrors at a speed $u$. Then,the man $M_2$ at $O$ will be able to see the image of $M_1$ for a total time of:

Assertion : $A$ concave mirror and convex lens both have the same focal length in air. When they are submerged in water,they will have same focal length.
Reason : The refractive index of water is smaller than the refractive index of air.

$A$ camera objective has an aperture diameter $d.$ If the aperture is reduced to diameter $d/2,$ the exposure time under identical conditions of light should be made