# 菲涅耳方程

## 简介

### s 和 p 偏振

1. 偏振入射光的电场分量与入射光及反射光所形成的平面相互垂直。此时的入射光状态称为「s偏振态」，源于德语「垂直（senkrecht）」。
2. 偏振入射光的电场分量与入射光及反射光所形成的平面相互平行。此时的入射光状态称为「p偏振态」，源于德语「平行（parallel）」。

## 光强方程

${\displaystyle \theta _{\mathrm {i} }=\theta _{\mathrm {r} }}$

${\displaystyle {\frac {\sin \theta _{\mathrm {i} }}{\sin \theta _{\mathrm {t} }}}={\frac {n_{2}}{n_{1}}}}$

${\displaystyle R_{s}=\left[{\frac {\sin(\theta _{t}-\theta _{i})}{\sin(\theta _{t}+\theta _{i})}}\right]^{2}=\left({\frac {n_{1}\cos \theta _{i}-n_{2}\cos \theta _{t}}{n_{1}\cos \theta _{i}+n_{2}\cos \theta _{t}}}\right)^{2}=\left[{\frac {n_{1}\cos \theta _{i}-n_{2}{\sqrt {1-\left({\frac {n_{1}}{n_{2}}}\sin \theta _{i}\right)^{2}}}}{n_{1}\cos \theta _{i}+n_{2}{\sqrt {1-\left({\frac {n_{1}}{n_{2}}}\sin \theta _{i}\right)^{2}}}}}\right]^{2}}$

${\displaystyle R_{p}=\left[{\frac {\tan(\theta _{t}-\theta _{i})}{\tan(\theta _{t}+\theta _{i})}}\right]^{2}=\left({\frac {n_{1}\cos \theta _{t}-n_{2}\cos \theta _{i}}{n_{1}\cos \theta _{t}+n_{2}\cos \theta _{i}}}\right)^{2}=\left[{\frac {n_{1}{\sqrt {1-\left({\frac {n_{1}}{n_{2}}}\sin \theta _{i}\right)^{2}}}-n_{2}\cos \theta _{i}}{n_{1}{\sqrt {1-\left({\frac {n_{1}}{n_{2}}}\sin \theta _{i}\right)^{2}}}+n_{2}\cos \theta _{i}}}\right]^{2}}$

${\displaystyle R=|r|^{2},}$ ${\displaystyle T={\frac {n_{2}\cos \theta _{t}}{n_{1}\cos \theta _{i}}}|t|^{2}}$[4]

${\displaystyle R=R_{s}=R_{p}=\left({\frac {n_{1}-n_{2}}{n_{1}+n_{2}}}\right)^{2}}$
${\displaystyle T=T_{s}=T_{p}=1-R={\frac {4n_{1}n_{2}}{\left(n_{1}+n_{2}\right)^{2}}}}$

## 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 [2010-01-13]. ISBN 0521642221. （原始内容存档于2021-02-20）.
3. ^ Jackson, J D. Classical Electrodynamics (3rd). New York: Wiley. 1999. ISBN ISBN 0-471-30932-X.
4. ^ Hecht (2002), p. 120.