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Question

A ray of light from a denser medium strikes a rare medium at an angle of incidence i (see figure). The reflected and refracted rays make and angle of 90 with each other. The angles of reflection and refraction are r and r. The critical angle is
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A
sin1(tan r)
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B
sin1(tan i)
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C
sin1(tan r)
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D
tan1(sin i)
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Solution

The correct option is A sin1(tan i)
As the reflected and refracted rays are at 900 then the angle of refraction is 90i

According to Snell's law,

sin i×μr=sin(90i)

μr=cot i

Critical angle is sin11μr=sin11cot i=sin1(tan i)

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