Question

When passing from a slower region into a faster region, it is possible for a wave to experience Total Internal Reflection (TIR): for certain angles, the entire wave will be reflected, with no transmitted portion. Using Snell’s law, solve for the critical angle of incidence θi, at which TIR begins to occur by setting the transmitted angle equal to 90 degree . Then, use this value to find the reflection coefficient R at the critical angle.

Answer 1

According to Snell's law

where are the refractive index of the medium through which incident and refracted rays pass

The angles are incident and refracted angles

At critical angle

Hence

Since sine of angle is always less than 1, this means

Therefore for Total internal reflection to occur,

Therefore the critical angle of incidence is

Suppose the light is being refracted from an optically dense medium to air, then

Then

The reflection coefficient of s polarised wave is

At critical angle

Therefore the reflection coefficient becomes