Question

Define the terms critical angle and total internal reflection. State two conditions necessary for total internal reflection to occur. Write down the relation for the critical angle in terms of refractive index.

Answer 1

Critical angle is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90o.
Total internal reflection: When a ray of light travelling from an optically denser medium to an optically rare medium is incident at an angle greater than the critical angle for the pair of media in contact, the ray is totally reflected back into the denser medium. This phenomenon is referred as total internal reflection.
The two necessary conditions for total internal reflection to take place are:
1.    The light ray must proceed from denser to rarer medium.
2. Angle of incidence in denser medium should be greater than the critical angle for the pair of media in contact.
Relation between critical angle and r.i.: The critical angle can thus be calculated by taking the inverse-sine ratio of speed of light in denser medium and the speed of light in rarer.

i_c = sin ^-1 `(("n"gamma)/("n"_i))`