Waves/Light

Light

Light moves in a vacuum at a speed of $c_{vac}=3\times 10^8\text{ m}{\text{ s}}^{-1}$. In transparent materials it moves at a speed less than $c_{vac}$ by a factor $n$ which is called the refractive index of the material:

$c=c_{vac}/n.$

Often the refractive index takes the form

$n^2\approx 1+\frac{A}{1-(k/k_R{)}^2},$

where $k$ is the wavenumber and $k_R$ and $A$ are constants characteristic of the material. The angular frequency of light in a transparent medium is thus

$\omega =kc=\frac{k{c}_{vac}}{n}\approx \frac{k{c}_{vac}}{\sqrt{1+A}}(1+\frac{1}{2}\frac{A}{1+A}\frac{k^2}{k_R^2})$

so the frequency increases slightly with increasing k. Typically, when k is near k_R, the material becomes opaque.

Ultimately, this is due to resonance between the light and the atoms of the materials.

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