For the given incident ray as shown in figure, for the condition of total internal reflection of this ray, the minimum refractive index of prism will be:-
A
√3+12
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B
√2+12
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C
√32
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D
√76
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Solution
The correct option is C√32 By Snell's law 1×sin45∘=μsin(90∘−θC) 1√2=μcosθC...(i) For second surface 1μ=sinθC...(2) Also, sin2θC+cos2θC=1
cosθC=√1−sin2θC put in (1) 1√2=μ×√1−1μ2⇒1√2=√μ2−1 √12+1=μ⇒μ=√32