Question

A beam of white light is incident on the surface of a diamond at an angle θa. (Figure 1) The index of refraction actually depends on the light's wavelength, so the different colors that comprise white light will spread out as they pass through the diamond (like in a prism). The index of refraction in diamond is nblue=2.450 for blue light while the indices of refraction for the lower frequency colors are all smaller. Thus, as shown in the figure, the blue and red light are refracted at different angles inside the diamond. A diamond is cut such that the angle between its top surface and its bottom surface is α. For α = 38 degrees, find the largest possible value of the incident angle θa such that the blue light is totally internally reflected off the bottom surface.

          A beam of white light is incident on the surface of a diamond at an angle θa. (Figure 1) The index of refraction actually depends on the light's wavelength, so the different colors that comprise white light will spread out as they pass through the diamond (like in a prism). The index of refraction in diamond is nblue=2.450 for blue light while the indices of refraction for the lower frequency colors are all smaller. Thus, as shown in the figure, the blue and red light are refracted at different angles inside the diamond. 
A diamond is cut such that the angle between its top surface and its bottom surface is α. For α = 38 degrees, find the largest possible value of the incident angle θa such that the blue light is totally internally reflected off the bottom surface.

Added by Joe W.

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