$A$ point source $S$ is placed at a distance of $15 \; cm$ from a converging lens of focal length $10 \; cm$. Where should a concave mirror of focal length $12 \; cm$ be placed so that a real image is formed on the object itself (in $; cm$)?

$A$ light ray is incident,at an incident angle $\theta_{1}$,on the system of two plane mirrors $M_{1}$ and $M_{2}$ having an inclination angle $75^{\circ}$ between them (as shown in figure). After reflecting from mirror $M_{1}$,it gets reflected back by the mirror $M_{2}$ with an angle of reflection $30^{\circ}$. The total deviation of the ray will be $\dots$ degree.

$A$ satisfactory photographic print is obtained when the exposure time is $10 \, s$ at a distance of $2 \, m$ from a $60 \, cd$ lamp. The time of exposure required for the same quality print at a distance of $4 \, m$ from a $120 \, cd$ lamp is $... \, s$.

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.

Ray optics is valid when characteristic dimensions are:

$A$ movie projector forms an image $3.5 \ m$ long of an object $35 \ mm$ long. Supposing there is negligible absorption of light by the aperture,what is the ratio of the illuminance on the slide to the illuminance on the screen?