If c is the speed of light in air and v is the speed of light in a medium, how is the refractive index nm of that medium defined?
nm = c/v
The absolute refractive index of a medium tells how much light slows down in that medium compared with its speed in vacuum (practically the same as in air). It is defined as the ratio of the speed of light in air to the speed of light in the medium.
So \(n_m = \frac{c}{v}\), where c is the speed of light in air and v is its speed in the medium. Since light travels slower in any material medium (\(v \lt c\)), the refractive index is greater than 1; for example, it is about 1.33 for water and about 1.5 for glass.
Being a ratio of two speeds, the refractive index has no unit. A product c×v or a difference c – v would carry units (m2/s2 or m/s), so neither can define this dimensionless quantity.
The inverted ratio v/c would always be less than 1 and would decrease as the medium becomes optically denser, which is the opposite of how refractive index behaves.
Hence, nm = c/v.
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