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Dispersion of white light in a prism

Dispersion is the splitting up of white light into its individual wavelengths, what we see as colors. Dispersion occurs with transparent surfaces that are not parallel to each other, such as gemstone facets. Measurement of dispersion is done (in gemology) by calculating the difference of refraction indices for red light waves and violet light waves.

The source for red light travels at a wavelength of 686.7nm (named the Fraunhofer B-line) and at 430.8nm for violet light (the Fraunhofer G-line). The interval between red and violet gives the dispersion value of a gemstone.

All the individual wavelengths have their own refractive index numbers. Red light has a lower refraction index than violet light, thus the violet part of white light will bend more. These values are different for all gemstones, dependent upon the stone's optical density (how fast light can travel inside the gemstone). All transparent gemstones will show dispersion, but the dispersion colors may be masked by the body color of the gemstone. In Diamonds, the color dispersion of white light causes the spectacular "fire" in well-cut brilliant cuts that possess good white color. This "fire" is an interaction between color dispersion and total internal reflection.

"Fire" in Diamond as the result of 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. The value for red light (nB) in a Diamond is measured at 2.407 and for violet light (nG) it is measured at 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 example shows that decreasing (shorter) wavelengths have increasing indices of refraction. This is known under the term Normal dispersion of the refractive indices.


Image of a Euromex table spectrometer
(Courtesy of Euromex)

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, and 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. One will however need to create a graph with calibration plates for the particular refractometer to correct the errors.

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