Question

Light is incident at an angle of 45 degrees on the surface of a diamond. The index of refraction of diamond is 2.42. Recall that the index of refraction for air is n↓air = 1. Find the angle of refraction. Answer in units of degrees

Answer 1

The angle of refraction is approximately 17.41 degrees.

Step-by-step explanation:

To find the angle of refraction, we can use Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction of the two media.

The formula is:

n₁ * sin(θ₁) = n₂ * sin(θ₂)

Given:

n₁ (index of refraction of air) = 1

n₂ (index of refraction of diamond) = 2.42

θ₁ (angle of incidence) = 45 degrees

Substituting the values into the formula, we have:

1 * sin(45°) = 2.42 * sin(θ₂)

sin(45°) is equal to √2 / 2, so the equation becomes:

(√2 / 2) = 2.42 * sin(θ₂)

Now we can solve for sin(θ₂):

sin(θ₂) = (√2 / 2) / 2.42

sin(θ₂) ≈ 0.2901

To find the angle of refraction, we take the inverse sine (sin⁻¹) of the value:

θ₂ ≈ sin⁻¹(0.2901)

θ₂ ≈ 17.41 degrees

Therefore, the angle of refraction is approximately 17.41 degrees.