A ray of monochromatic light is incident on one refracting face of a prism of angle `75^(@)`. It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the material of the prism is `sqrt(2)`, the angle of incidence on the first face of the prism is

Options

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 `90^@`
D. The angle between the incident ray and the emergent ray is `120^@`.

Answer

A, B, C

Explanation

Critical angle of material of prism, `C = sin^-1((1)/(mu)) = sin^-1((1)/(sqrt(3)))`
For refraction at face `AB`
`mu = (sin 60^@)/(sin r)`
or `sin r = (sin 60^@)/(mu) = (sqrt(3)//2)/(sqrt(3)) = (1)/(2)`
`r = 30^@`
`:. /_ BPQ = 90^@ + 30^@ = 120^@`
Hence, refracted ray goes along `PQ`. It meets the face `CD` at angle of incidence `= 45^@`
As `sin^-1(1)/(sqrt(2)) gt sin^-1 (1)/(sqrt(3))`
therefore, the ray `PQ` meets the face `CD` at an angle of incidence greater than critical angle. Hence, total internal reflection takes place at face `CD` of prism. The ray goes along `OQ` and meets the face `DA` at an angle of incidence `30^@`. The emergent ray `RT` will go making an angle of emergence `60^@` The incident ray `OP` and emergent ray `RT` will be inclined at an angle `90^@`.
Choices (a,b,c) are correct.
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