Question

A beam of white light is incident on the surface of a diamond at an angle θaθatheta_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. The indices of refraction in diamond are nred=2.410nred=2.410 for red light and nblue=2.450nblue=2.450 for blue light. The surrounding air has nair=1.000nair=1.000. Note that the angles in the figure are not to scale.

Calculate vredvredv_red, the speed of red light in the diamond. To four significant figures, c=2.998×108m/sc=2.998×108m/s.

Calculate vbluevbluev_blue, the speed of blue light in the diamond. To four significant figures, c=2.998×108m/sc=2.998×108m/s.

Derive a formula for δδdelta, the angle between the red and blue refracted rays in the diamond.

Express the angle in terms of nrednredn_red, nbluenbluen_blue, and θaθatheta_a. Use nair=1nair=1. Note that any trig function entered in your answer must be followed by an argument in parentheses, and that the proper way to enter the inverse sine of xxx in this case is asin(x).

Answer 1