The Physics
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Index of Refraction of Ruby and Sapphire

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Bibliographic Entry Result
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Reed, Rick. Refraction of Light. University of Missouri-Columbia, 1998.
Ruby 1.760
Rutile 2.62
Sanidine 1.522
Sapphire 1.760
St-Laurent, Sebastien. Shaders for Game Programmers and Artists. 2004.
Mercury 1.62
Ruby 1.76
Diamond 2.42
Bruesselbach, Hans W., Alexander A. Betin, and David S. Sumida. High Gain Laser Amplifier. US Patent 6646793, 2003. "In the illustrative embodiment, the first crystal is a square-cross-sectioned parallelepiped of Yb:YAG, having an index of refraction of approximately 1.82, and the second crystal is several pieces of sapphire with an index of approximately 1.78, surrounding the Yb:YAG…. As is known in the art, Yb:YAG has an index of refraction n1 = 1.82 and Sapphire is a birefringent material having an average index of refraction n2 = 1.78." 1.78
Draper, John Christopher. A Textbook of Medical Physics. 1885.
Sulphur 2.115
Sapphire 1.794
Ruby 1.779
Sapphire Properties. General Ruby & Sapphire Co. 2007.
Refractive Index:
0.3 Micron 1.814
0.4 1.785
0.7 1.763
1.0 1.757
2 Micron 1.740
3 1.713
4 1.677
5 1.623
Ruby Properties. General Ruby & Sapphire Co. 2007.
Refractive index at 700 nm 1.7638 Ordinary Ray
  1.7556 Extraordinary Ray
Birefringence 0.008
Refractive Index vs. Chromium Concentration 3 × 10−3 (Δn/% Cr2O3)

Ruby and sapphire are 2 of the 4 most valued precious gemstones in the world. (The other two are diamond and emerald.) They are both corundum which is a crystal form of aluminum oxide (Al2O3). While rubies only range from light pink to blood red in color, sapphires are all of the other colors. For rubies, price can range from affordable to very expensive. It is dependent upon its color, blood red being the most expensive, and its clarity, the clearer the better. The same goes for sapphires except that instead of blood red, blue is the most expensive.

The color difference in rubies and sapphires is due to inclusions, or small structural irregularities. One way to change the color is by using heat treatment. These stones are heated at temperatures of 1300°C to 1800°C in 20 to 30 minutes to change their color. The heat treatment causes these inclusions, or small structural irregularities, in the stones to reform themselves and improve the color by making them either darker, lighter, more intense, or a completely different color.

Refraction of light waves is due to the change in speed of light. When light travels from one medium to another, there may be a speed change which would then cause the light to bend and go in a different direction. Refraction is described by Snell's Law.

n1sin(θ1) = n2sin(θ2).


n1 is the index of refraction of the original medium that light was traveling in,
n2 is the index of refraction of the new medium that the light travels in,
θ1 is the angle of incidence which is between the ray of light and the normal,
θ2 is the angle of refraction which is also between the ray of light and the normal.

The index of refraction of a medium is a constant which measures the slowness of light in that medium. The definition of index of refraction is

n = c/v


c is the speed of light, approximately 3 × 108 m/s,
v is the speed of light in the medium,
n is the index of refraction.

n > 1 because the velocity of light in the medium will never be faster or going the same speed as if it were traveling in a vacuum.

Ruby has two indices of refraction because a single light ray is split into two light rays which travel at different velocities when entering the stone. The extraordinary ray, a beam of light that varies in wavelength, enters ruby with an index of refraction of 1.762. The ordinary ray, a beam of light that doesn't vary in wavelength, enters ruby with an index of refraction of 1.770. Materials with two indices of refraction are called birefringent.

The index of refraction for ruby for an extraordinary ray is 1.76 and for an ordinary ray is 1.77. The index of refraction for sapphire is sapphire is 1.77.

Gary Chang -- 2007