Hardness is a measure of how easily a mineral is scratched.
Mohs Scale of Hardness orders minerals from the softest (1 Talc) to the hardest (10 diamond). A mineral that has a specific hardness can scratch any mineral that has a lower hardness. The hardness scale is not linear. Quartz (hardness 7) is 100 times harder than talc and a diamond (hardness 10) is 1600 times harder than talc.
Hardness is not resistance to breaking. Diamonds are very hard, but they chip relatively easy. You can chip a diamond hitting it on a drinking glass, but the diamond will easily scratch the glass.
Specific gravity is covered under weight in the 4Cs.
Refractive index is one of the main ways of identifying a gemstone. The refractive index (RI) is an optical property that is the ratio of the speed of light through a vacuum to the speed of light through a transparent medium. Light is bent as it moves from air into a transparent material. This effect can be seen when putting a straight rod half-way in water and the rod appears to be bent.
Gemstones with a higher refractive index tend to be more brilliant. Light is bent at a higher angle when it enters a cut gemstone with a higher refractive index and thus more light is reflected back out the top. For example diamond has a high refractive index.
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