Question

A flat thin film of material of defined refractive index and thickness (n= 1.2, t = 800 nm) lies on top of a liquid (n=2.3) and is probed by an EM wave in the liquid. The other side of the film is exposed to air. What would be the minimum angle of incidence, in radians, that the incoming wave would need to have in order to enter the film but not pass through it?

Answer 1

For the wave to remain in the film only it has to undergo Total Internal Reflection. Then let angle of incidence to be at film-air interface be C(known as critical angle). Then at this angle, angle of refraction will be 90 degrees.

Hence using Snell's Law,

  

  

This critical angle will be equal to the angle of refraction of the film-liquid interface. Thus we can say that

The let "i" be the angle of incidence that the incoming wave from liquid to film need to have in order to enter the film but not to pass through it.

then again using Snell's Law,

  

  

  

(ANS)