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

Question

A beam of white light is incident on the surface of a diamond at an angle ??. (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. For example, the indices of refraction in diamond are nred 2.410 for red light and nblae 2.450 for blue light. Thus, blue light and red light are refracted at different angles inside the diamond as shown in the picture. The surrounding air has T2air1.000. Note that the angles in the figure are not to scale Now consider ec, the angle at which the blue refracted ray hits the bottom surface of the diamond. If ? is larger thanthe critical angle rit. the light will not be refracted out into the air, but instead it will be totally internally reflected back into the diamond. Find Berit Express your answer in degrees to four significant figures. bluen

Explanation / Answer

Answer:

Let us consider T=teta.

Now consider Tc, the angle at which the blue refracted ray hits the bottom

surface of the diamond. If Tc is larger than the critical angle Tcrit, the

light will not be refracted out into the air, but instead it will be totally

internally reflected back into the diamond.

Tcrit = asin(1/n)

Tcrit = asin(1/2.450)

Tcrit = 24.09

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