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Question

A wave has velocity v in medium P and velocity 2v in medium Q. If the wave is incident in medium P at an angle of 30o, then the angle of refraction will be

A
30o
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B
45o
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C
60o
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D
90o
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Solution

The correct option is D 90o
Let the absolute refractive index of medium P and medium Q are np and nq respectively.
Given:
The velocity of the wave in medium P is v
The velocity of the wave in medium Q is 2v
Angle of incidence i=30o in medium P
The angle of refraction r=? in medium Q
From the definition of the refractive index, we can write,
np=cv and nq=c2v
Thus, npnq=2vv=2
Now, from Snell's law we know, npsin i=nqsin r
npnq=sin rsin i
2=sin rsin 30o
sin r=2×12=1
sin r=sin 90o
r=90o

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