# Waves/Light

Waves : 1 Dimensional Waves
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#### Light

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

${\displaystyle c=c_{vac}/n.}$

Often the refractive index takes the form

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

where ${\displaystyle k}$  is the wavenumber and ${\displaystyle k_{R}}$  and ${\displaystyle A}$  are constants characteristic of the material. The angular frequency of light in a transparent medium is thus

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

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

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

Waves : 1 Dimensional Waves
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Examples - Problems - Solutions - Terminology