Question

A beam of light coming from a rarer medium is partially reflected from the surface of a denser medium and partially refracted into the denser medium. If the reflected and the refracted rays are perpendicular to each other and the ratio of the refractive indices of denser and rarer medium is 3, the angle of refraction will be

Answer 1

μ₂/μ₁ = sin i/ sin r'

∠r + ∠r' + 90° = 180° ( angle on a straight line)

so, ∠r + ∠r' = 90°

∴ ∠r = 90° - ∠r'           - (1)

Also,   ∠i =  ∠r ( by laws of reflection)

∴ μ₂/μ₁ = sin r/ sin r'

putting (1) in the above equation we get,

μ₂/μ₁ = sin (90-r')/ sin r'

⇒ μ₂/μ₁ = cos r'/ sin r' = 1/tan r' = cot r'

now, μ₂/μ₁ = 3 ( given)

putting this in the above obtained equation, we get,

cot r' = 3

∴ r' = cot⁻¹ 3 = 18.434°