A light beam containing red and violet wavelengths is incident on a slab of quartz at an angle of incidence of 45.0°. The index of refraction of quartz is 1.455 at 660 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.

To find the dispersion of the slab, we need to determine the angles of refraction for both red and violet light and then calculate the difference between the two angles.

Given:
Angle of incidence (θ₁) = 45.0°
Index of refraction for red light (n₁) = 1.455
Index of refraction for violet light (n₂) = 1.468

To find the angle of refraction, we can use Snell's Law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the indices of refraction: n₁sinθ₁ = n₂sinθ₂

For red light:
n₁sinθ₁ = n₂sinθ₂
1.455sin45.0° = 1.468sinθ₂

To solve for θ₂, we rearrange the equation:
sinθ₂ = (1.455/1.468)sin45.0°

Using a calculator, we find:
sinθ₂ = 0.99172

Taking the inverse sine:
θ₂ = sin^(-1)(0.99172)
θ₂ ≈ 80.0°

For violet light, we repeat the same steps:
n₁sinθ₁ = n₂sinθ₂
1.455sin45.0° = 1.468sinθ₂

sinθ₂ = (1.455/1.468)sin45.0°

Using a calculator, we find:
sinθ₂ = 0.99295

Taking the inverse sine:
θ₂ = sin^(-1)(0.99295)
θ₂ ≈ 80.7°

The dispersion is the difference between the angles of refraction:
Dispersion = θ₂ (violet) - θ₂ (red)
Dispersion = 80.7° - 80.0°
Dispersion ≈ 0.7°

Therefore, the dispersion of the slab is approximately 0.7°.