# 菲涅耳方程

## 简介

### s 和 p 偏振

1. 电场分量与偏振光入射波与反射波形成的平面垂直。此时平行光的状态称为s偏振态，源于德语senkrecht.
2. 电场分量与偏振光入射波与反射波形成的平面平行。此时平行光的状态称为p偏振态，源于德语perpendicular.

## 光强方程

$\theta_\mathrm{i} = \theta_\mathrm{r}$

$\frac{\sin\theta_\mathrm{i}}{\sin\theta_\mathrm{t}} = \frac{n_2}{n_1}$

$R_s = \left[ \frac{\sin (\theta_t - \theta_i)}{\sin (\theta_t + \theta_i)} \right]^2 =\left(\frac{n_1\cos\theta_i-n_2\cos\theta_t}{n_1\cos\theta_i+n_2\cos\theta_t}\right)^2 =\left[\frac{n_1\cos\theta_i-n_2\sqrt{1-\left(\frac{n_1}{n_2} \sin\theta_i\right)^2}}{n_1\cos\theta_i+n_2\sqrt{1-\left(\frac{n_1}{n_2} \sin\theta_i\right)^2}}\right]^2$

$R_p = \left[ \frac{\tan (\theta_t - \theta_i)}{\tan (\theta_t + \theta_i)} \right]^2 =\left(\frac{n_1\cos\theta_t-n_2\cos\theta_i}{n_1\cos\theta_t+n_2\cos\theta_i}\right)^2 =\left[\frac{n_1\sqrt{1-\left(\frac{n_1}{n_2} \sin\theta_i\right)^2}-n_2\cos\theta_i}{n_1\sqrt{1-\left(\frac{n_1}{n_2} \sin\theta_i\right)^2}+n_2\cos\theta_i}\right]^2$

$R=r^2\ \mathrm{and}\ T=\left(\frac{n_2\cos\theta_t}{n_1\cos\theta_i}\right)t^2$ [4]

$R = R_s = R_p = \left( \frac{n_1 - n_2}{n_1 + n_2} \right)^2$
$T = T_s = T_p = 1-R = \frac{4 n_1 n_2}{\left(n_1 + n_2 \right)^2}$

## 参考文献

1. ^ Hecht (1987), p. 100.
2. ^ Max Born; Emil Wolf. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (7th Edition) (Hardcover). Cambridge University Press. October 13, 1999: 334. ISBN 0521642221.
3. ^ Jackson, J D. Classical Electrodynamics (3rd). New York: Wiley. 1999. ISBN ISBN 0-471-30932-X.
4. ^ Hecht (2002), p. 120.