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Q.

A ray of light is incident at an angle i from denser to rare medium. The reflected and the refracted rays are mutually perpendicular. The angle of reflection and the angle of refraction are respectively r and r’, then the critical angle will be

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a

sin−1(sinr)

b

sin−1tanr′

c

sin−1(tani)

d

tan−1(sini)

answer is C.

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Detailed Solution

DμR=sinisinr′⇒RμD=sinr′sini=1sinC ⇒sinC=sinisin(90−r)=sinicosr=sinicosi ( as ∠i=∠r) ⇒sinC=tani⇒C=sin−1(tani)
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