Question

State the condition of total internal reflection to take place at an interface separating two transparent media. Hence derive the expression for the critical angle in terms of speed of light in two media.

Answer 1

Conditions for total internal reflection. There are two conditions to be satisfied for the total internal reflection to take place:

(i) Ray of light should proceed from optically denser to optically rarer medium.

(ii) Angle of incidence must be greater than the critical angle for the pair of media.

If a and b are optically rarer and optically denser media respectively, and C is the critical angle, then

sin C = \(\frac{1}{a} =\ ^b\mu_a\)

or sin C = \(\frac{v_b}{v_a}\)

= \(\frac{\text {velocity in optically denser medium }}{\text{velocity in optically rarer medium }}\)