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Question

A ray of light from a denser medium strikes the plane boundary of a rarer medium at an angle of incidence I . The angle of refraction is r . If the reflected and the refracted rays are mutually perpendicular the critical angle of the medium is :

A
sin1(cotI)
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B
sin1(tanI)
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C
tan1(sinI)
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D
sin1(tanr)
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Solution

The correct option is C sin1(tanI)
Angle between reflected ray and refracted ray is 90o
so according to diagram r1+r2+90o=180or1+r2=90o
in question r2=r
from law of reflection i=r1, substituting values in above equation
i+r=90o where r is angle of refraction.
From Snell's Law, n2sini=n1sinr
n.sini=sinr
n.sini=sin90oi
n.sini=cosi
n=coti
we know θcric=sin11n
putting n=coti
θcric=sin11coti
θcric=sin1tani
Hence option B is correct

1637573_1757937_ans_b3871bd1154345378dbddc28a54e489f.png

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