$A$ ray of light originates from inside a glass slab and is incident on its inner surface at an angle $\theta$ as shown below. In this experiment,the location $x$ of the spot where the ray hits the screen is recorded. Which of the following correctly shows the plot of variation of $x$ with the angle $\theta$?

$A$ water-proof laser pointer of length $10 \,cm$ is placed in a water tank. It rotates about a horizontal axis passing through its centre of mass in a vertical plane as shown in the figure. The time period of rotation is $60 \,s$. Assuming the water to be still and no reflections from the surface of the tank, the duration for which the light beam escapes the tank in one time period is close to ............. $s$. (Take, refractive index of water $= 1.33$)

$A$ prism has a refractive index of $1.5$. If a light ray undergoes total internal reflection at the interface with a liquid,what is the maximum possible refractive index of the liquid? (Refer to the provided diagram for geometry).

The wavelengths of light in two liquids $x$ and $y$ are $3500 \, \mathring{A}$ and $7000 \, \mathring{A}$ respectively. The critical angle of $x$ with respect to $y$ is .......... $^o$.

It is found that electromagnetic signals sent inside a glass sphere from $A$ towards $B$ reach point $C$. The speed of electromagnetic signals in glass cannot be:

$A$ ray of light incident normally on an isosceles right-angled prism travels as shown in the figure. The least value of the refractive index of the prism must be