Question

The refractive index of diamond is much greater than that of glass. Does a diamond cutter use this fact?

Answer 1

The refractive index of diamond relative to air is 2.42, which is considerably higher than that of ordinary glass, which is 1.5. As a result, the critical angle for total internal reflection in diamond, calculated as `[C = \sin^{-1}(1/n)]`, is approximately 24°, whereas in glass it is about 42°. This means the range of angles of incidence for total internal reflection inside diamond extends from 24° up to 90°, which is significantly wider than the 42° to 90° range in glass. Diamond cutters take advantage of this large range of angles by skillfully cutting the various faces of a diamond so that the light entering undergoes multiple internal reflections before exiting. This results in the sparkling effect seen in diamonds, a feature that arises because the light is reflected many times inside the diamond before coming out.

Hence, the fact that diamond has a much higher refractive index than glass is indeed utilized by diamond cutters to enhance the brilliance of the gemstone through total internal reflection within the diamond facets.