Final answer:
Diamonds sparkle from a combination of dispersion and total internal reflection. Light enters easily but is internally reflected due to the diamond's facets and high refractive index, only escaping at specific angles, which creates a concentrated sparkle. Dispersion causes the separation of light into multiple colors.
Step-by-step explanation:
A high-quality diamond sparkles with flashes of brilliant color when illuminated by white light primarily due to dispersion of light and total internal reflection. Diamonds have a high index of refraction, which means light enters easily but has trouble exiting due to a critical angle of only 24.4°. Consequently, light undergoes many internal reflections within the diamond before it can escape at certain places, leading to a concentrated sparkle. Furthermore, the diamond's facets are crafted to reinforce this effect. Dispersion occurs when different wavelengths of light refract at different angles, causing the separation of white light into a spectrum of colors, similar to the phenomenon of a rainbow.