Consider a light ray crossing a boundary from a substance in which the speed of light is c1 to a substance in which the speed of light is c2.Using the same theory as on the previous card gives sini/sinr = c1/c2 where i is the angle between the incident ray and the normal and r is the angle between the refracted ray and the normal.

This equation may be rearranged as (1/c1)sini = (1/c2)sinr

Multiplying both sides of this equation by c, the speed of light in a vacuum, gives (c/c1)sini = (c/c2) sinr.

Substituing n1 for (c/c1) where n1 is the refractive index of substance 1, and n2 for (c/c2) where n2 is the refractive index of substance, gives Snell's Law: n1sinθ1 = n2sinθ2 where θ1 = i and θ2 = r.

The speed of light in air at atmospheric pressure is 99.97% of the speed of light in a vacuum.

Therefore, the refractive index of air is 1.0003. For most purposes, the refractive index of air may be assuemd to be 1.

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