A right angle prism`(45^(@) - 90^(@) - 45^(@))` of refractive index n has a plane of refractive index `n_(1)(n_(1) ltn)` cemented to its diagonal face. The assembly is in air. The ray is incident on AB.

(i) Calculate the angle of incidence at AB for which the ray strikes the diagonal face at the critical angle .
(ii) Assuming n = 1.352 , calculate the angle of incidence at AB for which the refracted ray passes through the diagonal face undeviated.

Answer

(i)`e = sin^(-1) (1)/(sqrt(2)) [(sqrt(n^(2) - n_(1)^(2)))- n_(1)]` (ii) `sin^(-1)(0.956)`

Explanation

(i) Given that `r_(2) = C implies r_(1) = 45^(@) - C` & sin e = n sin`(45^(@)-C)`
sin e = n(`"sin"45^(@) "cos"45^(@) "sin"C`)
`implies e = sin^(-1) (1)/(sqrt(2)) (sqrt(n^(2)-n_(1)^(2)) - n_(1))`
(ii) to pass refracted ray undeviated `r_(2) = 0 implies r_(1) = 45^(@)` and sin e = n sin `45^(@)`
`implies e = sin^(-1) ((1.352)/(sqrt(2))) = sin^(-1)(0.956)`