$A$ light source is located at $P_1$ as shown in the figure. All sides of the polygon are equal. The intensity of illumination at $P_2$ is $I_0$. What will be the intensity of illumination at $P_3$?

$A$ small fish,$0.4\,m$ below the surface of a lake,is viewed through a simple converging lens of focal length $3\,m$. The lens is kept at $0.2\,m$ above the water surface such that the fish lies on the optical axis of the lens. The image of the fish seen by the observer will be at $\left( \mu_{water} = \frac{4}{3} \right)$

In a grease spot photometer,light from a lamp with a dirty chimney is exactly balanced by a point source at a distance of $10 \, cm$ from the grease spot. On cleaning the chimney,the point source is moved by $2 \, cm$ to obtain balance again. The percentage of light absorbed by the dirty chimney is nearly......$\%$

When sunlight falls normally on Earth,a luminous flux density (illuminance) of $1.57 \times 10^5 \; lm/m^2$ is produced on Earth. The distance of Earth from the Sun is $1.5 \times 10^8 \; km$. The luminous intensity of the Sun in candela is:

$A$ biconvex lens $(R_1 = R_2 = 30 \ cm)$ has a focal length equal to the focal length of a concave mirror. What is the radius of curvature of the concave mirror (in $cm$)? (Refractive index of the material of the lens $\mu = 1.6$)

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.