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A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 60º as shown in figure. If the refractive index of the material of the prism is 3 , which of the following is(are) correct ?

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a
The ray gets totally internally reflected at face CD.
b
The ray comes out through face AD
c
The angle between the incident ray and the emergent ray is 90º
d
The angle between the incident ray and the emergent ray is 120º

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detailed solution

Correct option is A

Applying Snell’s law at face AB, we get
1×sin60=3×sinr32=3sinr or sinr=12r=sin112=30sinθc=13
(where, θc is the critical angle)
θc=sin113 or θc35
From geometry, angle of incidence at Q is 45º. At face CD angle of incidence is greater than θc. Therefore, the rays gets totally internally reflected at face CD. Hence, option (a) is correct. From geometry, angle of incidence at R is 30º. At face AD angle of incidence is less than θcSo, the ray comes through face AD. Hence option (b) is correct. Applying Snell’s law at face AD, we gete=sin132=60
The angle between the incident ray and the emergent ray is 90º.
Hence, option (c) is correct and option (d) is incorrect

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