Explain total internal reflection from the laws of refraction.

For minimum deviation ${\mathrm{\delta }}_{\mathrm{m}}$, assuming that the angle of incident= angle of emergence , show that the refractive index of the material of the prism is ,

$\mathrm{\mu }=\frac{\sin \left\{{\displaystyle \frac{{\mathrm{\delta }}_{\mathrm{m}}+\mathrm{A}}{2}}\right\}}{\sin \left({\displaystyle \frac{\mathrm{A}}{2}}\right)}$, where $\mathrm{A}$ is the refractive angle of the prism.