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Question

Let the refractive index of a denser medium with respect to a rare medium be N12 and its critical angle θC . At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is 90o. Angle A is given by :

A
tan1(sinθC)
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B
1tan1(sinθC)
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C
1cos1(sinθC)
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D
cos1(sinθC)
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Solution

The correct option is A tan1(sinθC)
n12=ndnr

sinθsin90=n2n3

sinisinR=n2n1

sini=sinr

sinrsinR=n2n1=sinθcsin90

sinrcosr=sinθc

cosr

tanr=sinθc

r=tan1(sinθc)

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