Final answer:
The refractive index of a gem affects the degree to which light is refracted, or bent, as it passes through the gem. The path of light changes and is more significantly bent in a medium with a higher refractive index, like a diamond, causing the gem to sparkle.
Step-by-step explanation:
The refractive index (RI) of a gem relates to light as it passes through different mediums. When light enters a gemstone with a higher refractive index than the medium it's traveling from, the light is bent towards the normal, a line perpendicular to the surface at the point of contact. Conversely, if light leaves the gem and enters a medium with a lower refractive index, it bends away from the normal. This bending of light is known as refraction. It's important to notice that when comparing two mediums, the angle of refraction is less in the medium with the higher refractive index.
For instance, a diamond has a high refractive index compared to air, which results in light being bent significantly towards the normal as it enters and moves away from it as it leaves, contributing to its sparkling appearance. This is especially pronounced due to the large critical angle of diamonds, focusing outgoing light to specific points that then appear to sparkle.
Light reflecting from a medium also involves the refractive index but in a different way, as reflected light is not subject to the same refraction principles as it is not transmitted through the medium. Total internal reflection, which occurs in mediums like diamonds, happens when light strikes the medium boundary at an angle larger than the so-called critical angle. As a result, no light passes through and all light is reflected back into the medium, a property which can help a diamond to sparkle.