Two identical prism of index `sqrt3` are kept as shown in the figure. A light ray strikes the first prism at face AB. Find,
(a) the angle of incidence, so that the emergent ray from the first prism has minimum deviation.
(b) through what angle the prism DCE should be rotated about C so that the final emergent ray also has minimum deviation. `

Answer

A, B, C

Explanation

(a) For minimum deviation of emergent ray from the first prism. MN is parallel to AC
`:'``angleBMN=60^circ`
`:'` `angler=30^circ`
Applying Snell's law at M
`mu=(sini)/(sinr)`
`sini=musinr`
`sini=sqrt3xxsin30^circ=(sqrt3)/(2)` `impliesi=60^circ`
(b) When the prism DCE is rotated about C in anticlockwise direction by `60^circ`, as shown in the figure, then the final emergent ray SR becomes parallel to the incident ray TM. Thus, the angle of deviation becomes zero.