This is not an amethyst! This pretty lavalier is set with a garnet/glass doublet.
And what, you ask, is that? Well. A garnet/glass doublet is an assembled stone consisting of a thin crown of garnet, usually almandine, fused or glued to a colored glass
pavilion.
They were developed to imitate amethyst, peridot, tourmaline, and other transparent gems popular in the last half of the 19th century. Amethyst in particular was scarce and expensive. Russia was the major source of amethyst until it was discovered in Brazil in the nineteenth century, causing the price to drop. Queen Charlotte owned an amethyst bracelet which was valued at £2000 at the beginning of the 18th century and only £100 two hundred years later.
Why use garnet? Garnet is the only stone which will easily fuse to glass. Garnet has a hardness approximately equal to that of amethyst, and greater than that of glass, so the garnet cap keeps the top of the 'stone' from scratches. And, even though the garnet is red, the cap is so thin that doublets can be made in any color, even colorless. Looking at the stone from the top, the color is determined by the color of the glass.
The birthstone for January is the garnet. To most people, this means the dark red stone, as shown in this ring, but garnets are an incredibly diverse group of gems. At least eleven major types of garnet are known, ranging in color from colorless to black, and including yellow, orange, and green.