A light wave travelling linearly in a medium of dielectric constant 4, incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be :
(Given : relative permeability of medium μᵣ = 1)

Solution

Physics sir · 4 steps

Get the refractive index from the dielectric constant, find the critical angle, then go beyond it.

1. Refractive index. For a medium with dielectric constant εᵣ and relative permeability μᵣ, the refractive index is n = √(εᵣ μᵣ) = √(4 × 1) = 2.
2. Critical angle. Light is going from the denser medium (n = 2) into air (n = 1). Total internal reflection is possible, and it starts at the critical angle C.

   sin C = 1/n = 1/2 ⇒ C = 30°

3. Condition for TIR. All the light is reflected back only when the angle of incidence is greater than 30°. At 10° and 20° some light refracts into air. At exactly 30° the refracted ray just grazes along the surface.
4. So. Of the options, only 60° is greater than 30°, so the answer is (d).

The idea to keep. Use n = √(εᵣ μᵣ) when you are given a dielectric constant. Total internal reflection needs the angle of incidence strictly greater than the critical angle, with sin C = 1/n.

Answer from the NTA final answer key. Solution by PrepWiser.