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 incedent ray and emergent ray is `90^(@)`
D. The angle between the incedent ray and emergent ray is `120^(@)`

Answer

A, B, C

Explanation

By refraction at face `AB` :
`1.sin60^(@)=sqrt3. sinr_(1)`
So `r_(1)=30^(@)`
This shows that the refracted ray is parallel to side `BC` of prism. For side `'CD'` angle of incidence will be `45^(@)` , which can be calculated from quadrilateral `PBCQ` .
`sqrt3 sin 45^(@)=1 sinr_(2)`
So `sin r_(2)=(sqrt3)/(sqrt2)`
which is impossible. So, there will be `T.I.R.` at face `CD`.
Now, by geometry angle of incidence at `AD` will bat `30^(@)`. So angle of emergence will be `60^(@)` . Hence, angle between incident and emergent beams is `90^(@)`