A diamond is cut such that the angle between its top surface and its bottom surf

Question

A diamond is cut such that the angle between its top surface and its bottom surface is alpha. A beam of white light is incident on the surface of a diamond at an angle. 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 = 2.410 for red light, and rblue = 2.450 for blue light. Note that the angles in the figure are not to scale. (i) For Thetaa = 450, calculate 6, the angle between the red and blue refracted rays in the diamond. (ii) Now consider Thetac, the angle at which the refracted ray hits the bottom surface of the diamond. If Thetac is larger than the critical angle Thetacritical, the light will be totally internally reflected back into the diamond. Find Thetacritical, for both red and blue light. (iii) For alpha = 45degree find the largest possible value of the incident angle Thetaa such that the red and blue light are totally internally reflected off the bottom surface.

Explanation / Answer

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.

Express your answer in degrees to four significant figures.

All you need to do here is incorporate the refractive index:

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

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