This method is an interesting method and a unique approach to the determination of indices of refraction. It has the huge advantage of requiring no special equipment at all, beyond a human eye. It does require a darkened room, a small bare filament light source, and much practice. By merely looking through a faceted gemstone at a tiny light source, one can learn to estimate the index of refraction by displacement of the image he sees, birefringence by image separation and dispersion by spectral color fringes on the image. This may well prove a useful skill for one who travels much or operates without standard gemological equipment.
All you need are your eyes and some clean hands.
Pick up a stone in question and hold it up very close to your eye so that you can look into the table. You must hold it very close without touching – almost like inserting a contact lens, but again not touching. Look literally through the stone at a distant source of light such as a lamp or light bulb. You will see a number of reflections of the distant light source as they bounce around within the stone.
Roll the stone around its axis and tilt it slightly while watching the reflections. Due to the refractive properties of gemstones, each reflection will to some extent appear as a small rainbow. This is a single one of those rainbows as it appears looking through a spinel at the filament of a clear light bulb about 6 feet away:
Depending on the gem material in question, that rainbow will have varying properties. If the gem is doubly refractive you are likely to see doubled or ghosted (rainbow) images. Because the gem may be cut in any orientation with respect to the crystal structure (which is responsible for these phenomena) you may have to examine the stone from a variety of angles to be sure whether it is doubly refractive or not.