$A$ prism having an apex angle $4^o$ and refractive index $1.5$ is located in front of a vertical plane mirror as shown in the figure. Through what total angle is the ray deviated after reflection from the mirror (in $^o$)?

$A$ light ray is incident on the surface of a sphere of refractive index $n$ at an angle of incidence $\theta_0$. The ray partially refracts into the sphere with angle of refraction $\phi_0$ and then partly reflects from the back surface. The reflected ray then emerges out of the sphere after a partial refraction. The total angle of deviation of the emergent ray with respect to the incident ray is $\alpha$. Match the quantities mentioned in $List-I$ with their values in $List-II$ and choose the correct option.

$List-I$	$List-II$
$(P)$ If $n=2$ and $\alpha=180^{\circ}$,then all the possible values of $\theta_0$ will be	$(1)$ $30^{\circ}$ and $0^{\circ}$
$(Q)$ If $n=\sqrt{3}$ and $\alpha=180^{\circ}$,then all the possible values of $\theta_0$ will be	$(2)$ $60^{\circ}$ and $0^{\circ}$
$(R)$ If $n=\sqrt{3}$ and $\alpha=180^{\circ}$,then all the possible values of $\phi_0$ will be	$(3)$ $45^{\circ}$ and $0^{\circ}$
$(S)$ If $n=\sqrt{2}$ and $\theta_0=45^{\circ}$,then all the possible values of $\alpha$ will be	$(4)$ $150^{\circ}$
	$(5)$ $0^{\circ}$

$A$ lamp rated at $100 \, cd$ hangs over the middle of a round table with diameter $3 \, m$ at a height of $2 \, m$. It is replaced by a lamp of $25 \, cd$ and the distance to the table is changed so that the illumination at the centre of the table remains as before. The illumination at the edge of the table becomes $X$ times the original. Then $X$ is

$A$ convex mirror of focal length $15 \ cm$ and a concave mirror of focal length $10 \ cm$ are placed facing each other at a distance of $40 \ cm$ apart. $A$ point object is placed between the mirrors on their common axis at a distance of $15 \ cm$ from the concave mirror. The position of the image formed by reflection at the convex mirror will be at a distance of ..... $cm$ from it.

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.

$A$ bulb of $100 \text{ W}$ is hanging at a height of $1 \text{ m}$ above the centre of a circular table of diameter $4 \text{ m}$. If the intensity at a point on its rim is $I_0$,then the intensity at the centre of the table will be: