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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

(where, ${\mathrm{\theta }}_{\mathrm{c}}$ is the critical angle)

From geometry, angle of incidence at Q is 45º. At face CD angle of incidence is greater than ${\mathrm{\theta }}_{\mathrm{c}}$. 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 ${\mathrm{\theta }}_{\mathrm{c}}$So, the ray comes through face AD. Hence option (b) is correct. Applying Snell’s law at face AD, we get$\mathrm{e}={\mathrm{sin}}^{-1}\left(\frac{\sqrt{3}}{2}\right)={60}^{\circ }$
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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