# 瑞利散射

5毫瓦綠色激光筆光束是在夜間可見的，部分原因是因為存在於空氣中的各種顆粒和分子的瑞利散射。

$I(\lambda)_{scattering} \propto \frac{ I(\lambda)_{incident}}{\lambda^4}$

## 推導

$\overline{P} = \sqrt{\frac{\mu_0}{\epsilon_0}} \frac{\omega^4}{12\pi c^2} |\mathbf{p}|^2$（見电偶極子幅射

$\mathbf{p} = \frac{q^2}{m(\omega_0^2 - \omega^2)} \mathbf{E} \approx \frac{q^2}{m \omega_0^2} \mathbf{E} \quad \mbox{if } \omega_0 \gg \omega$

$I = (1/2) \epsilon_0 c E_0 ^2$
• 按輻射強度定義有：
$d I = - n \overline{P} dx$

$dI / I = - \gamma dx$

$\gamma \propto \omega^4 \propto \lambda^{-4}$

## 參考

1. ^ Lord Rayleigh (John Strutt) refined his theory of scattering in a series of papers that were issued over a period of decades. Here is a partial list of those papers:
1. John Strutt (1871) "On the light from the sky, its polarization and colour," Philosophical Magazine, series 4, vol.41, pages 107-120, 274-279.
2. John Strutt (1871) "On the scattering of light by small particles," Philosophical Magazine, series 4, vol. 41, pages 447-454.
3. John Strutt (1881) "On the electromagnetic theory of light," Philosophical Magazine, series 5, vol. 12, pages 81-101.
4. John Strutt (1899) "On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue of the sky," Philosophical Magazine, series 5, vol. 47, pages 375-394.