$A$ fish in an aquarium,$30 \, cm$ deep in water,can see a light bulb kept $50 \, cm$ above the surface of water. The fish can also see the image of this bulb in the reflecting bottom surface of the aquarium. The total depth of water is $60 \, cm$. Then the apparent distance between the two images seen by the fish is $(\mu_w = 4/3)$.

Which of the following is $NOT$ involved in the formation of a secondary rainbow?

$A$ ray of light strikes a plane mirror at an angle of incidence $45^o$ as shown in the figure. After reflection,the ray passes through a prism of refractive index $1.5$,whose apex angle is $4^o$. The angle through which the mirror should be rotated if the total deviation of the ray is to be $90^o$ is

An electric lamp is fixed at the ceiling of a circular tunnel as shown in the figure. What is the ratio of the intensities of light at base $A$ and a point $B$ on the wall?

$A$ 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	$(4)$ $150^{\circ}$
	$(5)$ $0^{\circ}$

If the polarising angle of a piece of glass for green light is $54.74^o$,then the angle of minimum deviation for an equilateral prism made of the same glass is......$^o$ (Given $\tan 54.74^o = 1.414$)