Question

A light beam containing red and violet wavelengths is incident on a slab of quartz at an angle of incidence of 49.7°. The index of refraction of quartz is 1.455 at 600 nm (red light), and its index of refraction is 1.468 at 410 nm (violet light). Find the dispersion of the slab, which is defined as the difference in the angles of refraction for the two wavelengths.

Answer 1

Δθ = 0.3 °

Step-by-step explanation:

For this exercise we will use the law of refraction

n₁ sin θ₁ = n₂ sin θ₂

Where n₁ and n₂ are the refractive indices and θ are the incident and refracted angles

We apply this equation for each wavelength

Red λ = 600

The refractive index of air n₁ = 1

Let's calculate the angle of refraction (θ₂)

sin θ₂ = n₁ / n₂ sin θ₁

sin θ₂ = 1 / 1,455 sin 49.7

sin θ₂ = 0.52417

θ₂ = sin⁻¹ (0.52417)

θ₂ = 31.6 °

Violet λ = 410 nm

Sin θ₃ = 1 / 1,468 sin 49.7

θ₃ = sin⁻¹ (0.5195)

θ₃ = 31.3 °

The angle of dispersion is

Δθ = θ₃ - θ₂

Δθ = 31.6 - 31.3

Δθ = 0.3 °