A ray OP of monochromatic light is incident on the face AB of prism ABCD mear vertex B at an incident angle of `60degree` (see figure). If the refractive index of the material of the prism is `sqrt3`, which of the following is (are) are correct? `

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

We can apply Snell.s law at point P to calculate angle of refraction.
`rArr" "mu sin theta="const"`
`rArr" "1xxsin 60=sqrt3xx sinr`
`rArr" "sinr=(1)/(2)`
`rArr" "r=30^(@)`
Hence ray PQ will be parallel to BC and hence cannot strike on this surface.
We can refer ray diagram to understand that light ray strikes on the surface CD at an angle `45^(@)` with the normal as shown. We know that for refractive index 1.5, critical andle is `42^(@)` and hence for refractive index 1.732 it will be even smaller and hence light ray will suffer internal reflection at point Q and will be incident on surface AD at point R at an angle `30^(@)` and will be refracted at an angle `60^(@)` following Snell.s law. First rotation at point P is `30^(@)` anticlockwise and then there is `90^(@)` clockwise rotation at point Q and then clockwise rotation at point R by an angle `30^(@)`, hence net deviation suffered by the light ray is `90^(@)` clockwise. Hence angle between incident ray and emergent ray is `90^(@)`. Finally we can see that options (a), (b) and (c) are correct.