Final answer:
Faceted crystals like diamonds exhibit sparkle due to total internal reflection and a high index of refraction, critical angle manipulation through faceting, and light dispersion.
Step-by-step explanation:
Faceted crystals, such as diamonds, are produced under conditions that promote total internal reflection and feature a large index of refraction. The specific angle at which light can no longer exit the crystal is called the critical angle, which for a diamond-to-air surface is only 24.4°.
Facets are the flat surfaces on a crystal cut in such a way to make light's exit at angles less than the critical angle unlikely, thus trapping light within to create multiple internal reflections. High-quality diamonds are exceptionally clear, enabling light to travel within, strike the internal surfaces numerous times, and exit concentrated at a few optimal points, giving rise to the diamond's characteristic sparkle. Additionally, colors observed in diamonds are often not due to the gem's inherent color, which is typically nearly colorless, but a result of dispersion, and in the case of colored diamonds, due to structural defects and minute inclusions.