A beam consisting of red, blue and yellow colours is incident normally on the face AB of an isosceles right angled prism ABC as shown in Fig. 6.5. Complete the diagram to show the refracted and the emergent rays. Given that the critical angle of glass-air interface for yellow colour is `45^(@)`

Explanation

The completed diagram is shown in Fig. 6.6. The beam is incident normally `(angle i = 0^(@))` on the face AB so it passes without deviation `(angle r = 0^(@))` for all colours and with no dispersion. Now the refracted beam inside the prism, strikes the face AC at an angle of incidence equal to `45^(@)`. Since the critical angle for yellow colour at the glass-air interface is `45^(@)`, so the yellow colour suffers refraction along the face AC of the prism `(angle r = 90^(@))`.
The critical angle for the light of red colour will be more than `45^(@)`
`(since sin C=1/mu and mu_(r)
Now the critical angle for the light of blue colour will be less than `45^(@)` since `mu_(B)>mu_(Y)` so the light of blue colour is incident on the glass-air surface AC at an angle of incidence greater than the critical angle for blue colour. Therefore, the light of blue colour suffers total internal reflection and strikes normally on the base BC of the prism. It then emerges out of the prism without deviation. Thus blue colour emerges out of the prism at right angle to its incident direction.