Question

PQR is a prism of angle θ (= sin^-1 0.8). The refractive index, μ , of the prism is given by

μ = 1.20 + \(\frac{8\times10^5}{λ^2}\)

λ is wave - length of incident light.

AB is a ray of λ = 400 nm while ray CD has λ = 500 nm. The two rays are incident as shown in Fig. Which of the following statements is correct?

(1) Both rays AB and CD, emerge out of face PR

(2) Ray AB does not emerge out, but ray CD emerges out, from face PR

(3) Ray AB emerges out, but ray CD does not emerge out of face PR

(4) Neither ray AB nor ray CD, emerges out of face PR

Answer 1

(3) Ray AB emerges out, but ray CD does not emerge out of face PR

Let μ₁ and μ₂ the, respective, refractive indices of the prism for rays AB and CD. Then

The angle of incidence of both rays on face PR is θ. The critical angle, i₁ and i₂ , for wavelengths λ₁ and λ₂ , are

Therefore, ray AB undergoes T.I. R on face QR and does not emerge out. For ray CD, angle of incidence θ is less than the critical angle i₂ . This ray emerges out of race QR.