Waves/Light

Waves : 1 Dimensional Waves
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Light

Light moves in a vacuum at a speed of $c_{vac}=3\times 10^{8}{\mbox{ m}}{\mbox{ s}}^{-1}$. 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

$\omega =kc={\frac {kc_{vac}}{n}}\approx {\frac {kc_{vac}}{\sqrt {1+A}}}(1+{\frac {1}{2}}{\frac {A}{1+A}}{\frac {k^{2}}{k_{R}^{2}}})$

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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Waves : 1 Dimensional Waves
1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13
Examples - Problems - Solutions - Terminology