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3x5 is the standard size as it closely follows the golden ratio
The chemical composition of ruby is aluminum oxide (Al 2 O3). Its specific gravity is 3.99 to 4.00 and refractive index range is 1.760-1.768 to 1.770-1.779. Ruby's hardness on Mohs scale is 9. It's the next hardest mineral after diamond.
When a ray of light passes from material 1 to material 2: N1 sin θ1 = N2 sin θ2 where N1 & N2 are the refractive indices of the materials, and θ1 is the angle of incidence, θ2 the angle of refraction. From air to the material: N1 = 1.00, θ1 = 40°, θ2 = 50°, N2 = unknown, the index of refraction of the material: → 1.00 x sin 50° = N2 x sin 40° → N2 = 1.00 x sin 50° ÷ sin 40° → N2 ≈ 1.1917 (the index of refraction of the material)
the index of a cube root is 3.