A gem is a naturally occuring material desirable for its beauty

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 A gem is a naturally occuring material desirable for its beauty, valuable in its rarity, and sufficiently durable to give lasting pleasure.
  • It should be naturally occuring, but it need not be crystalline. 
  • Beauty is determined by brilliance, iridescence, color, sparkle, and play of color.
  • A gem should be durable against heat and common household chemicals.  It should not be easily scratched or broken.  Brittleness is a measure of the gem's tendency to crack or cleave.
  • How rare is rare?:
    • Typically, a diamond deposit yields about 5g gem/1000kg of mined material.  That's 5g per million grams!
Beauty of a gemstone is determined by brilliance, luster, fire and color (later lecture).  The first three quantities depend on the cut of the stone.  Before we can understand why cut gems sparkle, we need to learn some basic terms to describe cut stones.
Cut stone vocabulary:
·         Polished planar surfaces are referred to as facets.
·         The midline of a facetted gem is called the girdle and may or may not be facetted.
·         The area above the girdle is called the crown; the factes on the crown are the table, the star facets, the kite (or bezel) facets and the upper girdle facets.
·         The area below the girdle is called the pavillion; these facets are known as the lower girdle facets, the pavilion facets and the culet.
·         The type of cut where gems have a flat bottom surface and a rounded upper surface is called cabochon.
Why are gems cut the way they are?
·         Reflection and refraction
In order to understand why gems are faceted, it is essential to understand how light behaves once it passes into a gemstone.
Light can either be reflected off a surface or pass through the surface into the new substance.
When light passes from one material into another, it is bent or refracted. But by how much?
The amount light is bent is determined by the density difference between the gem and air. A measure of the amount light is bent is termed the "refractive index" or 'RI'.
·         The Critical Angle
The critical angle is the angle at which total internal reflection is achieved. But what do we mean by "internal reflection"?
Light travelling through a stone intersects the stone-air surface. If it passes within the critical angle (measured relative to the normal to that surface), it will exit the stone. If it passes outside the critical angle, it will be internally reflected.

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We use these facts to determine how facets should be placed in order to control the path of light in a gemstone!
Naturally, in order to achieve brilliance and sparkle, we do NOT want light to escape from the pavillion. We DO want light to escape from the top facets!
Thus, to recap, the placement of facets on a gem is determined using critical angle information, which comes from the refractive index information.
Many gem cuts that meet the basic critical angle requirements can be created.
Two important examples are the "Brilliant Cut" and "Emerald Cut".
For this course, we are not concerned about how facets are created in practice. However, take a look here if you are curious!
Not only does the placement of the facets matter, but the smoothness of the surface (called "luster") does too. Luster is a function of both the surface and the RI of the mineral itself. Terms used to describe luster include adamantine, pearly, metallic, silky, vitreous, resinous, and waxy. Gem grading reports refer to "finish" or "polish" to describe how well polished the surface is. "Luster" is also used to describe how mirror=like the surface of a pearl is.
·         When the surface of the gem is polished, the light is internally reflected, as expected.
·         If the surface of the gem is left rough, light is lost through unplanned leakage.
"Fire" refers to the rainbow-like flashes of color seen in cut stones.
Fire is especially obvious in diamonds
Another example: the rainbows should be obvious!
Where do these come from?
It is important to realize that the extent to which light is refracted (bent on passing into or out of the gem) is dependent upon the wavelength (color) of the light. Note that blue light is bent more than red light
The phenomenon of different amount of bending of different colored light is referred to as dispersion.
Dispersion is measured: 
dispersion = refractive index of violet - refractive index of red light.
Dispersion varies greatly with the mineral type. Lists of dispersion values are available
The fire of a gem is a consequence of the cut of the stone, coupled with its dispersion.
Many of the light behaviors we have thought about here (reflection, refraction, dispersion) are commonly observed in everyday life! Excellent examples can be found in the atmosphere.

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