The manner in which gemstones are cut is one of the more aesthetically important and pleasing applications of the principles of light reflection. Particularly in the case of diamonds, the beauty and economic value of an individual stone is largely determined by the geometric relationships of the external faces (or facets) of the gem. The facets that are cut into a diamond are planned so that most of the light that falls on the front face of the stone is reflected back toward the observer (Figure 6).
A portion of the light is reflected directly from the outside upper facets, but some enters the diamond, and after internal reflection, is reflected back out of the stone from the inside surfaces of the lower facets. These internal ray paths and multiple reflections are responsible for a diamond’s sparkle, often referred to as its “fire” . An interesting consequence of a perfectly cut stone is that it will show a brilliant reflection when viewed from the front, but will look darker or dull from the back, as illustrated in Figure 6.
Light rays are reflected from mirrors at all angles from which they arrive. In certain other situations, however, light may only be reflected from some angles and not others, leading to a phenomenon known as total internal reflection. This can be illustrated by a situation in which a diver working below the surface of perfectly calm water shines a bright flashlight directly upward at the surface.
If the light strikes the surface at right angles it continues directly out of the water as a vertical beam projected into the air. If the light’s beam is directed at a slight angle to the surface, so that it impacts the surface at an oblique angle, the beam will emerge from the water, but will be bent by refraction toward the plane of the surface. The angle between the emerging beam and the surface of the water will be smaller than the angle between the light beam and the surface below the water.
If the diver continues to angle the light at more of a glancing angle to the surface, the beam rising out of the water will get closer and closer to the surface, until at some point it will be parallel to the surface. Because of light bending due to refraction, the emerging beam will become parallel to the surface before the light below the water has reached the same angle. The point at which the emerging beam becomes parallel to the surface occurs at the critical angle for water. If the light is angled still further, none of it will emerge. Instead of being refracted, all of the light will reflect at the water’s surface back into the water just as it would at the surface of a mirror.