Week 11: Light 381
It is also pretty! Diamonds and the diamond-like compound C3 (Moissonite) haveex-
tremely large indices of refraction, roughlynd= 2.4. This makes its critical angle:θcd= sin−^1(
1
2. 4
)
= 24. 6 ◦ (934)
Light incident on the facet of a diamond at any anglegreaterthan this (rather small)
angle istrappedby the diamond. Diamonds are cut so that light entering through any
given facet is reflected many times without escaping, so that dispersion splits the light
up into many colors until it escapes either through the sides or at corners or edges. This
gives diamond (or Moissanite) its “bright and sparkly” appearance.Cut crystal prisms
and lesser clear gemstones have much the same properties on a lesser scale, trapping light
and splitting it up into a rainbow of colors to brighten an otherwise drab existence.Dispersion
1.521.51(^400500600700800)
1.53
λ(nm)
n
Index of refraction of glass
Figure 149: An approximate dispersion curven(λ) for “ordinary” glass. However, distinct glass
mixtures can have very different dispersion curves, including ones wherenincreaseswith increasing
wavelengthλ(decreases with frequency).
To better understand thecolorsproduced by diamond, or the colors in a rainbow, or the
color band produced from white light by a prism, we have to consider refraction from a
medium withdispersion. Dispersion, recall, describes the fact that the index of refrac-
tion for most materials isn’t really a constant, itvarieswith frequency/wavelength. Most
transparent materials have a dispersion in the visible range thatdecreases(increases)
the index of refraction withwavelength(frequency). A typical dispersion curve for the
kind of glass one might find in a drinking glass or prism is shown across the range of
visible wavelengths in figure 149. Note well that violet light (400 nm) has an index of
refraction that is a percent or two higher than the index of refraction of red light (700
nm).
This is sufficient to cause white light incident at some nonzero angle tosplit upinto its
distinct component wavelengths in beams that gradually spatially separate as the light
travels. The band of colors produced by any given source of incident light, sorted out
by wavelength fromlongest to shortestis called thespectrumof the incident light.
White light is a mixture of all visible colors, and its spectrum is the familiar“rainbow”
of colors, Red Orange Yellow Green Blue Indigo Violet, or “ROY G BIV” (a common
mnemonic for the order). Note well that the frequency order is opposite – fromsmallest
to largest.
One familiar way to get a good spatially separated band of colors is to use two refractive
surfaces, each of which helps to further bend the resolved colors– aprism.