The index of refraction of crown glass for red light is 1.513, while for blue light it is 1.531. White light is incident on the glass at 26.2◦.
Find the angle of refraction for red light. Answer in units of ◦.
Find the angle of refraction for blue light. Answer in units of ◦.
To find the angle of refraction for red light, we need to use Snell's law, which relates the angles of incidence and refraction to the indices of refraction of the two media.
Snell's law states:
n1 * sin(θ1) = n2 * sin(θ2)
Given:
Index of refraction for red light (n1) = 1.513
Angle of incidence (θ1) = 26.2°
We need to find θ2, the angle of refraction for red light.
Rearranging Snell's law:
sin(θ2) = (n1 / n2) * sin(θ1)
Substituting the values:
sin(θ2) = (1.513 / n2) * sin(26.2°)
Now, we can solve for θ2 by taking the inverse sine (arcsine) of both sides:
θ2 = arcsin((1.513 / n2) * sin(26.2°))
Now, let's substitute the value for the index of refraction of blue light (n2 = 1.531) and calculate the angle of refraction for red light:
θ2 = arcsin((1.513 / 1.531) * sin(26.2°))
Calculating the above expression will give us the angle of refraction for red light.
To find the angle of refraction for blue light, we follow the same process, but substitute the index of refraction for blue light (n1 = 1.531) into Snell's law and calculate the corresponding angle of refraction.
θ2 = arcsin((1.531 / n2) * sin(26.2°))
Calculating the above expression will give us the angle of refraction for blue light.