Horizontal rays of red light (λ = 660 nm, in vacuum) and violet light (λ = 410 nm, in vacuum) are incident on the flint-glass prism shown in the drawing. The indices of refraction for the red and violet light are nred = 1.662 and nviolet = 1.698. The prism is surrounded by air. What is the angle of refraction for each ray as it emerges from the prism? (Assume α = 22.8°.)

To find the angle of refraction for each ray as it emerges from the prism, we can use Snell's law, which relates the angle of incidence, angle of refraction, and the indices of refraction of two mediums.

The formula for Snell's law is:

n1 * sinθ1 = n2 * sinθ2

Where:
n1 = index of refraction of the medium the light is coming from (incident medium)
θ1 = angle of incidence
n2 = index of refraction of the medium the light is entering (refracted medium)
θ2 = angle of refraction

In this case, the incident medium is air (index of refraction ~ 1) and the refracted medium is the flint-glass prism.

Given values:
- λred = 660 nm (red light wavelength in vacuum)
- λviolet = 410 nm (violet light wavelength in vacuum)
- nred = 1.662 (index of refraction for red light)
- nviolet = 1.698 (index of refraction for violet light)
- α = 22.8° (angle of the prism)

First, let's calculate the angle of incidence for each ray based on the given angle of the prism.

θ1 = α

For the red light:
n1 = 1 (air)
n2 = nred
θ2 (red) = ?

For the violet light:
n1 = 1 (air)
n2 = nviolet
θ2 (violet) = ?

To solve for the angles of refraction, we need to rearrange Snell's law:

sinθ2 = (n1 * sinθ1) / n2

For the red light:
sinθ2 (red) = (1 * sinα) / nred

For the violet light:
sinθ2 (violet) = (1 * sinα) / nviolet

Now, we have the values to calculate the angles of refraction.

Using a scientific calculator:
For red light:
θ2 (red) = arcsin((1 * sinα) / nred)

For violet light:
θ2 (violet) = arcsin((1 * sinα) / nviolet)

Substituting the given values into the equations, we can find the angles of refraction for each ray.