Explain the phenomenon of total internal reflection in a right-angled prism.

At the interface between two materials having refractive indices $n_1$ and $n_2$,the critical angle for reflection of an electromagnetic wave is $\theta_{1C}$. The $n_2$ material is replaced by another material having refractive index $n_3$,such that the critical angle at the interface between $n_1$ and $n_3$ materials is $\theta_{2C}$. If $n_3 > n_2 > n_1$,$\frac{n_2}{n_3} = \frac{2}{5}$,and $\sin \theta_{2C} - \sin \theta_{1C} = \frac{1}{2}$,then $\theta_{1C}$ is:

The phenomenon involved in the reflection of radio waves by the ionosphere is similar to:

$A$ point source of light is kept below the surface of water $(n_{w} = 4/3)$ at a depth of $\sqrt{7} \ m$. The radius of the circular bright patch of light noticed on the surface of water is

$A$ vertical pencil of rays comes from the bottom of a tank filled with a liquid. When the tank is accelerated horizontally with an acceleration of $7.5\, m/s^2$,the ray is seen to be totally internally reflected by the liquid surface. What is the minimum possible refractive index of the liquid? (Take $g = 10\, m/s^2$)

'Mirage' is a phenomenon due to