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A ray OP of monochromatic light is incid...

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? `

A

The ray gets totally internally reflected at face`CD`

B

The ray comes out throughface`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 ray is `120^(@)`

Text Solution

Verified by Experts

The correct Answer is:
A,B,C
Taking refraction at`AB`
`1xx60^(@)=sqrt(3)"sin" r rArr "sin" r= (1)/(2) rArr r=30^(@)`
Taking refraction at`CD`
`i=45^(@)` and `"sin"C=(1)/(sqrt(3)) rArr C="sin"^(-1)(1)/(sqrt(3))`
at CD `igtC `,so T.I.R.happens `(sin^(-1)""(1)/(sqrt(3))ltsin ^(-1)""(1)/(sqrt(2)))`
Taking refraction at`AD`
`sqrt(3)xxsin30^(@)=1xx"sin"r implies "sin"r=(sqrt(3))/(2) rArr r=60^(@)`
` delta_("net")=delta_(1)+delta_(2)+delta_(3)`
` delta_("net")=(60-30)CW+(180-2xx45)CW+(60-30)ACW=90^(@)CW`
Net deviation is `90^(@)`
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