Why does a diamond sparkle?

The critical angle is the largest angle at which light
rays inside a diamond can escape.
The more a material bends light, the higher
the RI Refractive index, the smaller its critical angle. Because diamond has a high RI,
it has only a small critical angle, 24.5 degrees. This is the reaon why well-cut
diamonds can be so brilliant : with smaller critical angles, there is less opportunity
for light to exit, so there is more chance that the light reflects off the diamond's
inner surfaces several times before finally exiting through its crown (where you will
see it). Most, but not all of the light leaves it like that, it depends on the angle of
incidenece and degree of polarization. Light rays that reflect back into the diamond are
called secondary rays, and they contribute to a diamond's overall brilliance, fire and
scintillation. Some don't leave the diamond but lose energy or dissipate into the
crystal's structure.
On top, diamonds are harder, so take a better polish on
their facets, so they will reflect more light also than glass (glass windows will not
reflect as much as diamonds) : luster is also better, images including light will be
reflected better.