Consider a glass cube slab of dielectric bound by the planes x = 0 ,   x = a   ;   y = 0 ,   y = b   ;   z = 0 ,   z = c   ; with b > a > c . The slab is placed in air and has a refractive index of n . The minimum value for n , such that all rays entering the dielectric at y = 0 reach y = b is

Step-by-step solution

Planes bounding the dielectric are as shown below. Due to dielectric, a light ray incident at y = 0 , at some angle θ bends towards normal and it strikes plane x = a . If angle of incidence at x = a , is more than angle of critical incidence, TIR occurs and light ray, then emerges out of plane y = b . For TIR at x = a sin 90 ° - r = 1 n or cos r = 1 n . . . . i Also, n = sin θ sin r Now θ at y = 0 , varies from 0 ° to a maximum of 90 ° So, for limiting incidence, n = sin 90 ° sin r ⇒ n = 1 sin r . . . . ii From Eqs