Question

Two prisms of identical geometrical shape are combined with their refracting angles oppositely directed. The materials of the prisms have refractive indices 1.52 and 1.62 for violet light. A violet ray is deviated by 1.0° when passes symmetrically through this combination. What is the angle of the prisms?

Answer 1

Let A be the angle of the prisms.
Refractive indices of the prisms for violet light, μ₁ = 1.52 and μ₂ = 1.62
Angle of deviation, δ = 1.0°
As the prisms are oppositely directed, the angle of deviation is given by
δ = (μ₂ − 1)A − (μ₁ − 1)A
δ = (μ₂ −μ₁ )A
$$\begin{gathered} A=\frac{\delta }{{\mu }_2-{\mu }_1}=\frac{1}{(1.62)-(1.52)}=\frac{1}{0.1} \\ \Rightarrow A=10° \end{gathered}$$
So, the angle of the prisms is 10^∘.