Define critical angle for a given pair of media and total internal reflection. Obtain the relation between the critical angle and refractive index of the medium.

Definition ofCritical angle - When a ray of light passes from a denser to a rarer medium, the value of angle of incidence for which the angle of refraction becomes \(\displaystyle 90^{0}\) is called critical angle for that pair of media. Total internal Reflection - When a ray of light passes from a denser to rarer medium and the angle of incidence exceeds the critical angle for pair of media, the ray under goes reflection. This is called total internal reflection. \[\text { From Snell's law } \quad \frac{\sin i}{\sin r}=\mu_{r d} \] When angle of incidence is equal to critical angle \(\displaystyle \left(\angle i=\angle i_{c}\right), \angle r=90^{0}\)