A beam of white light is incident on the surface of a diamond at an angle a. (Fi

Question

A beam of white light is incident on the surface of a diamond at an angle a. (Figure 1) Since the index of refraction actually 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 index of refraction in diamond is nblue=2.450 for blue light. The indices of refraction for the lower frequency colors are all smaller. Thus, blue light and red light are refracted at different angles inside the diamond, as shown in the picture. (Not shown is the orange, yellow, and green light in between the red and the blue.)    Note that the angles in the figure are not to scale. A diamond will appear bluish in color if the blue light is internally reflected while the remaining colors are allowed to refract out.

Now consider c, the angle at which the blue refracted ray hits the bottom surface of the diamond. If c is larger than the critical angle crit, the light will not be refracted out into the air, but instead it will be totally internally reflected back into the diamond. Find crit.

Explanation / Answer

use,

theta_critical=sin^-(n_air/n_blue)

theta_critical=sin^-(1/2.45)

theta_critical=24.09 degrees

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