Imagine a cube of glass with polished facets. Cut off one corner to get a 3-sided pyramid, polish the triangular cut face, and you have a retroreflector. The points of the triangle leak light, but the central portion reflects. Like a gemstone pavilion, the prism doesn't have to be silvered to reflect but relies on the principle of total internal reflection.
You can purchase a retroreflector from an optical supplier, even on ebay. If you want to facet your own, here are the instructions:
The 6 girdle facets don't have to be polished. Here are some paths of light rays hitting a retroreflector:
The table facet is tilted with respect to the rays, so each ray gets refracted slightly as it passes through the table. Each ray hits each of the 3 "pavilion" facets that make up the corner cube. After the third bounce, its path is exactly parallel to its path when it entred the stone but displaced laterally. When a light ray exits, it gets refracted again by the same amount as when it entered, so each light ray leaves the prism exactly parallel to the path it entered. This is true regardless of the refractive index.
Now the pavilion angle of 54.74° is quite steep for a gemstone pavilion. You might think that if three facets are good, six would be better. What you will find is that light makes one bounce off a pavilion facet and then leaks out the other side. This high angle just does't work with your average conical pavilion.
One of the problems in gemstone design is light leakage when a stone is tilted. This is especially true for materials of low refractive index. The retroreflector continues to do its job even when tilted. This true partly because the three bounces can "share the load" better than with two bounces.
Now a retroreflector makes a lousy gemstone. The biggest problem is "head shadow" or viewer refection. All that you can see in the stone is your own reflection. Even if you tilt the stone, you still see your reflection. The light rays from lights get reflected back to their source instead of towards the viewer. The next problem is scintillation—three pavilion facets don't break up the light very much.
In the next post, we'll see how to borrow some of the good features of a retroreflector and use them to our advantage in gemstone design.
Most of this material was covered in an article by Paul W. Smith in Gerald Wykoff's American Gemcutter magazine, September, 1987 and in my article in the Newsletter of the Texas Faceters' Guild, Jan-Apr, 1996.
