The angle of incidence and the angle of refraction for light going from air into a material with a higher index of refraction are 69.9° and 39.6°, respectively. What is the index of refraction of this material?

To determine the index of refraction of a material, you can use Snell's law, which relates the angles of incidence and refraction to the indices of refraction of the two media involved.

Snell's law is given by: n1 * sin(theta1) = n2 * sin(theta2)

In this case, the light is going from air (with index of refraction n1 ≈ 1) into a material with a higher index of refraction, denoted as n2. The angle of incidence is given as θ1 = 69.9° and the angle of refraction as θ2 = 39.6°.

Let's plug the values into Snell's law and solve for n2:

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

1 * sin(69.9°) = n2 * sin(39.6°)

sin(69.9°) = n2 * sin(39.6°)

n2 = sin(69.9°) / sin(39.6°)

Using a calculator, we can find that sin(69.9°) ≈ 0.9405 and sin(39.6°) ≈ 0.6407. Dividing these values gives:

n2 ≈ 0.9405 / 0.6407

n2 ≈ 1.465

Therefore, the index of refraction of this material is approximately 1.465.