According to physics, why do diamonds sparkle?

The brilliant sparkle of a diamond occurs from refraction and the total internal reflection of light. The precisely cut surfaces of a diamond refract or redirect incoming light until it is reflected back out of the facets of the top to the observer's eyes.

Diamonds are graded based on their ability to return light, also known as performance. More light refracted through the top facet leads to higher the light performance and a higher grade for the diamond. If a diamond is cut too shallow or too deep, the light leaks out of the bottom of the diamond and reduces its brilliance.