Question

A parallel beam of light containing two wavelengths 1, and i, equal to 465 nm and 652-nm respectively enters an equilateral glass prism at angle of incidence i. What is the emergent angle for each wavelength?​

Answer 1

The emergent angle of the first wavelength is 25.53⁰.

The emergent angle of the second wavelength is 26⁰.

The angle each beam leave the the prism is calculated using Snell's law as follows;

$n_1 si n\theta _1 = n_2 sin\theta_2$

The emergent angle of the first wavelength is calculated as follows;

$sin(45) = 1.64sin\theta_1\\\\sin\theta _1 = \frac{sin(45)}{1.64} \\\\sin\theta _1 = 0.431\\\\\theta_1 = sin^{-1} ( 0.431)\\\\\theta_1 =25.53 ^0$

The emergent angle of the second wavelength is calculated as follows;

$sin(45) = n_2 sin(\theta_2)\\\\sin(45) = 1.62 sin(\theta_2)\\\\sin(\theta_2) = \frac{sin(45) }{1.62} \\\\sin(\theta_2) = 26^0$

"Your question is not complete, it seems be missing the following information";

A parallel beam of light containing two wavelengths, λ1 = 465 nm and λ2 = 652 nm, enters the silicate flint glass of an equilateral prism. At what angles, θ1 and θ2, does each beam leave the prism. Use n455nm = 1.64 and n642nm =1.62. The incident angle is 45⁰.

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