$A$ glass sphere of refractive index $1.5$ and radius $40\,cm$ has half its hemispherical surface silvered. The point where a parallel beam of light,coming along a diameter,will focus (or appear to) after coming out of the sphere,will be:

$1\%$ of light of a source with luminous intensity $50 \,cd$ is incident on a circular surface of radius $10 \,cm$. The average illuminance of the surface is: (in $,lux$)

$A$ concave mirror has a radius of curvature of $40\, cm$. It is at the bottom of a glass that has water filled up to $5\, cm$ (see figure). If a small particle is floating on the surface of water,its image as seen from directly above the glass is at a distance $d$ from the surface of water. The value of $d$ is close to ......$cm$ (Refractive index of water $= 1.33$)

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.

Write the names of instruments developed by the use of properties of reflection and refraction of mirrors,lenses,and prisms.

$A$ concave mirror is placed on a horizontal table with its axis directed vertically upwards. Let $O$ be the pole of the mirror and $C$ its centre of curvature. $A$ point object is placed at $C$. It has a real image,also located at $C$. If the mirror is now filled with water,the image will be