A parallel beam of light is incident from air at an angle α on the side PQ of a right angled triangular prism of refractive index n=2. Light undergoes total internal reflection in the prism at the face PR when α has a minimum value of 45°. The angle θ of the prism is
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a
15°
b
22.5°
c
30°
d
45°
answer is A.
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Detailed Solution
At A, 1sinπ4=μsinr⇒12=2sinr ⇒r=300 As αmin=π4,rmin=π6For TIR at B, θ+r≥θc ⇒θ+r≥sin−11μ⇒θ+r≥sin−112⇒θ+r≥π4 ⇒r≥π4−θ⇒rmin=π4−θ⇒π6=π4−θ⇒θ=150