What is total internal reflection. Explain the phenomenon using Huygen’s principle.

Total Internal reflection:
When light is refracted at the surface into the rarer medium, when the angle of incidence is greater than the critical angle $\left(\mathrm{i}>{\mathrm{\theta }}_{\mathrm{C}}\right.)$, then no light is refracted, and the entire incident light is reflected into the same denser medium. This phenomenon is known as the total internal reflection.
Total Internal Reflection on the basis of Huygens principle :
Consider refraction of a plane wave at a rarer medium. So V₂ > V₁. Similar manner, Construct a refracted wave front as shown in Fig. Now angle of refraction is greater than the angle of incidence.
By Snell’s Law ${\mathrm{\mu }}_1\sin \mathrm{i}={\mathrm{\mu }}_2\sin \mathrm{r}$

But $\sin {\mathrm{i}}_{\mathrm{c}}=\frac{{\mathrm{\mu }}_2}{{\mathrm{\mu }}_1}$
Where i_c = critical angle.
$\text{ If }\mathrm{i}={\mathrm{i}}_{\mathrm{c}}\text{ then }\mathrm{r}={90}^{\circ },\sin \mathrm{r}=1\text{, }$
$\text{ If }\mathrm{i}>{\mathrm{i}}_{\mathrm{c}}$ The ray turns back into the medium 1. Hence it is called total internal reflection