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.
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 known under the term Normal dispersion of the refractive indices.
Measurement of dispersion is usually carried out using a table spectrometer. Through the minimum deviation method, very accurate refraction indices can be obtained with this apparatus (more accurate than with the refractometer). This type of instrument can be obtained for around USD 1500.00, and takes some skill to operate.
An easier way to measure dispersion would be to use narrow bandpass interference filters on a refractometer. However, most refractometers are calibrated to take measurments on the sodium D-line, so the B and G lines may be hard to see for most humans.
Scientists usually measure dispersion between the C and the F lines, giving considerably different values. The values of these lines lay closer to what our eyes can distinguish, so measurements on the C and F lines may be valuable after interpolation to obtain the B and G line values.
Experimentation with narrow bandpass interference filters with wavelengths of 656nm (nC) and 486nm (nF) may give good results.