A light ray traveling through air strikes a smooth, flat slab of crown glass at an angle of 30 degrees to normal. Index of refraction for crown glass is 1.66. What is the angle of refraction?

To find the angle of refraction, we can use Snell's Law, which relates the angle of incidence and the angle of refraction to the refractive index of the materials involved.

According to Snell's Law:
n₁ * sin(θ₁) = n₂ * sin(θ₂)

Where:
n₁ = refractive index of the medium the light is coming from (in this case, air)
n₂ = refractive index of the medium the light is entering (in this case, crown glass)
θ₁ = angle of incidence
θ₂ = angle of refraction

Given:
n₁ = 1 (refractive index of air approximated as 1)
n₂ = 1.66 (refractive index of crown glass)
θ₁ = 30 degrees

Let's substitute these known values into Snell's Law and solve for θ₂:

1 * sin(30) = 1.66 * sin(θ₂)

Now, we can rearrange the equation to solve for θ₂:

sin(θ₂) = (1 * sin(30)) / 1.66

Using a calculator, evaluate the right side of the equation:

sin(θ₂) ≈ 0.2924

Now, take the inverse sine (sin⁻¹) of the value to find θ₂:

θ₂ ≈ sin⁻¹(0.2924)

Using a calculator to find the inverse sine, we get:

θ₂ ≈ 17.5 degrees

Therefore, the angle of refraction is approximately 17.5 degrees.