The diagram shwos five isosceles right angled prisms.A light ray incident at`90^(@)`at the first face emerge at same angle with the normal from the last face.Which of the following realtions will hold regarding the refractive indics?

Answer

`mu_(1)^(2)+mu_(3)^(2)+mu_(5)^(2)=2+mu_(2)^(2)+mu_(4)^(2)`

Explanation

`1xxsin90^(@)=mu_(1)sinr_(1)rArr1=mu_(1)sinr_(1)….(1)`
`mu_(1) cos r_(1)=mu_(2)sin r_(2) rArr mu_(2)sin r_(2)=mu_(1) cos r_(1)`...(2)
`mu_(2) cos r_(2)=mu_(3)sin r_(3) rArr mu_(2)sin r_(3)=mu_(3) cos r_(3)...(3)`
`mu_(3) cos r_(3)=mu_(4)sin r_(4) rArr mu_(4)sin r_(4)=mu_(3) cos r_(3)...(4)`
`mu_(4) cos r_(4)=mu_(5)sin r_(5) rArr mu_(4)sin r_(4)=mu_(5) cos r_(5)...(5)`
`mu_(5) cos r_(5)=mu_(6)sin r_(6) rArr=mu_(5) cos r_(5)...(6)`
FromEq(1) to(6)
`2+mu_(2)^(2)+mu_(4)^(2)=mu_(1)^(2)+mu_(3)^(2)+mu_(5)^(2)`