Question

A beam of white light is incident on the surface of a diamond at an angle θa. (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 nblue=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 nair=1.000. Note that the angles in the figure are not to scale. Part A Now consider θc, the angle at which the blue refracted ray hits the bottom surface of the diamond. If θc is larger than the critical angle θcrit, the light will not be refracted out into the air, but instead it will be totally internally reflected back into the diamond. Find θcrit. Express your answer in degrees to four significant figures

Answer 1

に) 6 ritical = sin-11 노 346 -1 2.450 24.07 Therefore the critical angle of the diamond is 24.070

Answer 2

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