Dispersion and Absorption of Light

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  • Permittivity of substance according to elementary theory of dispersion: $$\varepsilon = 1+\sum_limits_{k}\\frac{n_k e^2/m\varepsilon_0}{\oega^2_{0k}-\omega^2,$$ where $n_k$ is the concentration of electrons of natural frequency $\omega_{0k}$.
  • Relation between refractive index and permittivity of substance:$$n = \sqrt{\varepsilon}.$$
  • Phase velocity $v$ and group velocity $u$: $$v=\omega/k, u=d\omega/dk.$$
  • Rayleigh's formula: $$u=v=\lambda\frac{dv}{d\lambda}.$$
  • Attenuation of a narrow beam of electromagnetic radiation: $$I=I_0e^{-\mu d},$$ where $\mu = \varkappa+\varkappa^\prime, \mu, \varkappa, \varkappa^\prime$ are the coefficients of linear attenuation, absorption and scattering.

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