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, μ r = 1 )

Step-by-step solution

As given in the question, we can write μ 1 = ε r μ r = 2 . 8 × 1 = 2 . 8 and μ 2 = ε r μ r = 6 . 8 × 1 = 6 . 8 Now applying Snell's law and considering r = 90 ° - i , we get μ 1   sin   i = μ 2   cos   i ⇒ tan   i = μ 2 μ 1 = 6 . 8 2 . 8 ⇒ tan   i = 2 . 8 + 4 2 . 8 1 2 ⇒ i = tan - 1 1 + 10 7 1 2 Therefore, θ = 7 .