Red light (n = 1.520) and violet light (n = 1.538) traveling in air are incident on a slab of crown glass. Both colors enter the glass at the same angle of refraction. The red light has an angle of incidence of 26.50°. What is the angle of incidence of the violet light?

Apparently the two colors enter the glass at different incidence angles but have the same angle of refraction (A) inside the glass.

For the red light,
sin 26.5 = 1.520 sinA
Therefore
sin A = 0.2936
A = 17.07 degrees

For the violet light, with the same angle of refraction A
sin I = 1.538 sinA = 0.4516
I = 26.84 degrees

To find the angle of incidence of the violet light, 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 of the two media.

Mathematically, Snell's law can be written as:

n1 * sin(theta1) = n2 * sin(theta2)

Where:
n1 = index of refraction of the first medium (in this case, air)
theta1 = angle of incidence of the first medium (in this case, the red light's angle of incidence)
n2 = index of refraction of the second medium (in this case, crown glass)
theta2 = angle of refraction of the second medium (which we need to find for violet light)

Given:
n1 (air) = 1.000
n2 (crown glass) = 1.520
theta1 (red light's angle of incidence) = 26.50°

Let's plug in the values into Snell's law and solve for theta2:

1.000 * sin(26.50°) = 1.538 * sin(theta2)

sin(theta2) = (1.000 * sin(26.50°)) / 1.538

Now, we can find the inverse sine (arcsin) of both sides to find theta2:

theta2 = arcsin((1.000 * sin(26.50°)) / 1.538)

Using a calculator to evaluate this expression, the angle of incidence of the violet light is approximately 17.80°.

To solve this problem, we can use Snell's Law, which relates the angle of incidence, angle of refraction, and indices of refraction. Snell's Law is given by:

n₁ * sin(θ₁) = n₂ * sin(θ₂)

Where:
n₁ = index of refraction of the medium from which the light is incident (in this case, air)
n₂ = index of refraction of the medium to which the light is refracted (in this case, crown glass)
θ₁ = angle of incidence
θ₂ = angle of refraction

We have the following given information:
n₁ (air) = 1.000 (approximately)
n₂ (crown glass) = 1.520 (for red light) and 1.538 (for violet light)

For the red light, the angle of incidence (θ₁) is given as 26.50°.

We need to find the angle of incidence (θ₁) for the violet light.

Let's start by rearranging Snell's Law to solve for θ₂:

sin(θ₂) = (n₁ / n₂) * sin(θ₁)

Now, we can substitute the values into the equation and solve for θ₂:

For red light:
sin(θ₂) = (1.000 / 1.520) * sin(26.50°)
θ₂ (red light) ≈ 15.04°

Now, we can use the same formula for violet light, but this time we'll use the index of refraction for violet light (n₂ = 1.538) and the angle of refraction we just found for the red light (θ₂ ≈ 15.04°):

sin(θ₂) = (1.000 / 1.538) * sin(26.50°)
θ₂ (violet light) ≈ 24.27°

Therefore, the angle of incidence for the violet light is approximately 24.27°.