In the figure, light rays of blue, green and red wavelengths are incident on an isosceles right-angled prism. Explain, with reason, which ray of light will be transmitted through the face AC. The refractive indices of the prism for red, green and blue light are 1.39, 1.424 and 1.476 respectively.
Answer: Only the red ray is transmitted through AC; green and blue undergo total internal reflection.
Solution
At the hypotenuse AC the angle of incidence is 45∘. The ray can emerge only if 45∘<θc, i.e. if sin45∘<μ1, which means μ<sin45∘1=2≈1.414. ∙ Red: μ=1.39<1.414⇒ no TIR, \emph{transmitted}. ∙ Green (1.424) and Blue (1.476): μ>1.414⇒45∘>θc, \emph{total internal reflection} occurs.
