After hearing in class that diamonds and other gemstones are cut to maximize the

Question

After hearing in class that diamonds and other gemstones are cut to maximize the total internal reflectance to increase their brilliance (shine), you decide to check out the jewelry store in the mall. While looking around, you notice that the diamonds seem to sparkle with color, as well as white light. Trying to reconcile this with what you learned in class, you do some googling. Google informs you that this effect is known as dispersion, and is due to the fact that the index of refraction of a material depends on the wavelength of incident light. This is why a prism can create a rainbow from white light! Further googling informs you that the indices of refraction in diamond are nred = 2.410 for a particular wavelength of red light and nblue = 2.450 for a particular wavelength of blue light.

A. Focusing only on the blue light, what is the critical angle ?c, for the reflection of the bottom surface of the diamond, as shown in Figure 2?

B.     B. If the angle between the top surface and the bottom surface is ??=45

Explanation / Answer

critical angle c

sinc=1/n

n is the refractive index

nred=2.410

sinc=1/2.410

so we can find angle c

that is the angle of reflection

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