From The Gemology Project
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Dispersion of white light in a prism

Dispersion is the splitting up of white light in its indiviual wavelenghts (colors).
This happens on transparent surfaces (such as facets) that are not parallel to eachother and measurment is done (in gemology) by calculating the difference in refraction indices of red and violet light.
The source for red light travels at a wavelength of 686.7nm (named the Fraunhofer B-line) and 430.8nm for violet (the Fraunhofer G-line). The interval between red and violet gives the dispersion value of a gemstone.
The reason that this happens is that all the individual wavelengths have their own refractive index. For instance red light has a lower refraction index than violet light and thus the violet part of white light will bend more.
Those values are different for all gemstones, depending on their optical density.
All transparent gemstones will show dispersion, however the dispersion colors may be masked by the body color of the gemstone.

"Fire" in Diamond as the result of dispersion and total internal reflection

In Diamond the color dispersion of white light causes the spectacular "fire" in well cut brilliants that possess good white color.
This is an interaction between color dispersion and total internal reflection.

The refraction index of diamond (measured with nD - or the Fraunhofer D-line) gives a refraction index of 2.417. However for red light (nB) this is 2.407 and for violet light (nG) it is 2.451. The interval between the B and the G lines is 2.407 - 2.451 = 0.044. Thus the dispersion value of Diamond is 0.044.
This shows that decreasing wavelengths have increasing indices of refraction and this is know as the term Normal dispersion of the refractive indices.