Geometrical OpticsHard
Question
A ray of light from a denser medium strikes a rarer medium at an angle of incidence i (see figure). The reflected and refracted rays make an angle of 90o with each other. The angles of reflection and refrection are r and r′. The critical angle is
Options
A.sin-1 (tan r)
B.sin-1 (cot i)
C.sin-1 (tan r′)
D.sin-1 (sin i)
Solution
r + r′ + 90o = 180o
∴ r′ = 90o - r
Further
Applying Shell′s law, μD sin i = μR sin r′
or μDsin r = μR sin (90o - r) = μRsin r
∴
tan r, θ = sin-1 
= sin-1 (tan r) ∴ Correct option is (c).
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