The refractive index of a particle can be determined with microscope equipment for measuring interference in transmitted light. If the path difference is several wavelengths, white illumination will used. If the particle has strong dispersion, measurements made with white light give an apparent refractive index much higher than the true one. The apparent index is related to the group velocity of light waves in the substance in the same way that the true index is related to phase velocity. Flaky crystals of hematite showed apparent index 4.52, in agreement with theory, compared with the true ordinary index around 3.09.
William D. Ross, "Refractive Index Measurement by Interference Microscopy: Corrections for Dispersion," Appl. Opt. 11, 1916-1918 (1972)