A certain kind of glass has an index of refraction of 1.660 for blue light of wavelength 420 nm and an index of 1.630 for red light of wavelength 690 nm. If a beam containing these two colors is incident at an angle of 30.0° on a piece of this glass, what is the angle between the two beams inside the glass?

Explanation:

Using Snell's law

n₁ sinθ₁ = n₂ sinθ₂

for 420 nm wavelength

where n₁ = 1.00 ( refractive index of air) and θ₁ = 30° n₂ = 1.660

1.00 × sin 30° = 1.660 sinθ₂

sinθ₂ = 0.3012

θ₂ = sin⁻¹ 0.3012 = 17.53°

for 690 nm wavelength

n₁ sinθ₁ = n₂ sinθ₂

sinθ₂ = 0.5 / 1.630

θ₂ = sin⁻¹ 0.3067 = 17.86°

the angle between the two beam = 17.863° - 17.53° = 0.333°