Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are 2.8 (medium -1) and 6.8 (medium -2), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence should be tan ⁻¹( 1 + 10/θ )^(1/2) the value of θ is __________.
(Given for dielectric media, μᵣ=1)

Solution

Physics sir · 3 steps

Reflected and refracted rays at right angles means Brewster angle, and with μr = 1 the refractive index is √K.

1. Brewster condition. When the reflected and refracted rays are perpendicular, the light is incident at the Brewster angle i_B. At this angle tan i_B = n₂/n₁, where light goes from medium 1 into medium 2.
2. Index from K. For any medium n = √(εᵣ μᵣ). Here μᵣ = 1, so n = √K. That gives n₁ = √2.8 and n₂ = √6.8.

   tan i_B = √(6.8/2.8) = (17/7)^(1/2) = (1 + 10/7)^(1/2)

3. So. Matching with i_B = tan⁻¹(1 + 10/θ)^(1/2) gives θ = 7.

The idea to keep. Rays at 90° to each other is always the Brewster angle. If the data is given as dielectric constants, convert using n = √K before using tan i_B = n₂/n₁.

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