A right angles prism `(45^(@),90^(@), 45^(@))` of refractive index n has a plate of refractive index `(n_(1)ltn)` cemented to its diagonal face. The assembley is in air. A ray is incident on AB.
a. Calculate the angle of incidence at AB for which the ray strikes the diagonal face at the critical angle.
b. Assuming `n=1.351`, calculate the angle of incidence at AB for which the refracted rey 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)`