A diamond's index of refraction for red light, 656 nm, is 2.410, while that for blue light, 434 nm, is 2.450. Suppose white light is incident on the diamond at 32.2°. Find the angles of refraction for red and blue light.
red light?
blue light?
To find the angles of refraction for red and blue light, we can use Snell's Law, which relates the angles of incidence and refraction to the refractive indices of the materials involved.
Snell's Law is given by:
n1 * sin(theta1) = n2 * sin(theta2)
Where:
- n1 is the refractive index of the medium the light is coming from (in this case, air).
- theta1 is the angle of incidence.
- n2 is the refractive index of the medium the light is entering (in this case, diamond).
- theta2 is the angle of refraction.
We are given:
- n1 = 1 (since air has a refractive index close to 1)
- theta1 = 32.2°
- n2 for red light = 2.410
- n2 for blue light = 2.450
Let's first find the angle of refraction for red light:
Using Snell's Law, we have:
1 * sin(32.2°) = 2.410 * sin(theta2_red)
Rearranging the equation, we can solve for theta2_red:
sin(theta2_red) = (1 * sin(32.2°)) / 2.410
theta2_red = arcsin((1 * sin(32.2°)) / 2.410)
Using a scientific calculator, we find:
theta2_red ≈ 12.861°
Now, let's find the angle of refraction for blue light:
Using Snell's Law, we have:
1 * sin(32.2°) = 2.450 * sin(theta2_blue)
Rearranging the equation, we can solve for theta2_blue:
sin(theta2_blue) = (1 * sin(32.2°)) / 2.450
theta2_blue = arcsin((1 * sin(32.2°)) / 2.450)
Using a scientific calculator, we find:
theta2_blue ≈ 12.465°
Therefore, the angles of refraction for red light and blue light are approximately 12.861° and 12.465°, respectively.