The refractive index of the material of a triangular prism of apex angle φ = 4 ∘ is n 1 = 1.3 . The prism is an isosceles triangle. Another prism of apex angle 2 φ is attached to the previously de

Question

The refractive index of the material of a triangular prism of apex angle φ = 4 ∘ is n 1 ​ = 1.3 . The prism is an isosceles triangle. Another prism of apex angle 2 φ ​ is attached to the previously described one as shown in the figure. A beam of light enters the first prism, parallel to the base of the isosceles triangle. The light beam emerges parallel to the original beam. What is value of n 2 ​ ?

TestHub · Accepted Answer

The beam enters the first prism parallel to its base, hitting the first face at $\frac{ϕ}{2}$ ; inside, $θ = \frac{ϕ /2}{n _{1}} = \frac{2}{1.3}$ .

Incidence at the shared face: $α = ϕ - θ = 4 - \frac{2}{1.3} = \frac{3.2}{1.3}$ .

Emerging parallel to the original beam needs the deviations to cancel: $n_{1} α = n_{2} \frac{ϕ}{2}$ .

$1.3 \times \frac{3.2}{1.3} = n_{2} \times 2 \Rightarrow n_{2} = 1.60$

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