A beam of white light is incident on the surface of a diamond at an angle theta_

Question

A beam of white light is incident on the surface of a diamond at an angle theta_a. (Figure 1) Since the index of refraction depends on the light's wavelength, the different colors that comprise white light will spread out as they pass through the diamond. For example, the indices of refraction in diamond are n_red = 2.410 for red light and n_blue = 2.450 for blue light. Thus, blue light and red light are refracted at different angles inside the diamond, as shown in the picture. The surrounding air has n_air = 1.000. Note that the angles in the figure are not to scale. Now consider theta_c, the angle at which the blue refracted ray hits the bottom surface of the diamond. If theta_c is larger than the critical angle theta_crit, the light will not be refracted out into the air, but instead it will be totally internally reflected back into the diamond. Find theta_crit. Express your answer in degrees to four significant figures. A diamond is cut such that the angle between its top surface and its bottom surface is alpha. For alpha = 45 degree, find the largest possible value of the incident angle theta_a such that the blue light is totally internally reflected off the bottom surface. Express your answer in degrees to four significant figures.

Explanation / Answer

Part A

crit = asin(1/n)
crit = asin(1/2.450)
crit = 24.09°

24.09°

Part B

by subtracting the critical angle (Part A) from :

d = 45 – 24.09
d = 20.91

Now use Snell’s law:

sin(max) = 2.450 * sin(20.91)
sin(max) = 0.8744
max = 60.97°

60.97°

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