Three light rays red (R), green (G) and blue (B) are incident on a right-angled prism `abc' at face `ab'. The refractive indices of the material of the prism for red, green and blue wavelengths are 1.39, 1.44 and 1.47 respectively. Out of the three, which colour ray will emerge out of face `ac'? Justify your answer. Trace the path of these rays after passing through face `ab'.
Answer: Only the red ray emerges from face `ac'; green and blue undergo total internal reflection there.
Solution
At the hypotenuse `ac' the angle of incidence is 45∘. A ray emerges only if 45∘<θc, i.e. μ<sin45∘1=2≈1.414. ∙ Red (μ=1.39<1.414): emerges (refracts out of `ac'). ∙ Green (1.44) and Blue (1.47): μ>1.414, so 45∘>θc and they suffer \emph{total internal reflection}.
