# 几何光学

## 利用馬克士威方程組推導几何光学的三个原理

${\displaystyle E_{||,i}(x,y,0)+E_{||,r}(x,y,0)=E_{||,t}(x,y,0)}$

${\displaystyle E_{||,i}=E_{||,i0}\ e^{i\mathbf {k} _{i}\cdot \mathbf {r} -\omega t}}$
${\displaystyle E_{||,r}=E_{||,r0}\ e^{i\mathbf {k} _{r}\cdot \mathbf {r} -\omega t}}$
${\displaystyle E_{||,t}=E_{||,t0}\ e^{i\mathbf {k} _{t}\cdot \mathbf {r} -\omega t}}$

${\displaystyle k_{ix}x+k_{iy}y=k_{rx}x+k_{ry}y=k_{tx}x+k_{ty}y}$

${\displaystyle k_{ix}=k_{rx}=k_{tx}}$
${\displaystyle k_{iy}=k_{ry}=k_{ty}}$

${\displaystyle k_{i}\sin \theta _{i}=k_{r}\sin \theta _{r}}$

${\displaystyle n\ {\stackrel {def}{=}}\ {\frac {c}{v}}={\frac {ck}{\omega }}}$

${\displaystyle n_{i}\sin \theta _{i}=n_{t}\sin \theta _{t}}$

## 参考文献

1. ^ Moritz von Rohr, p2
2. ^ Moritz von Rohr, p4
3. ^ Griffiths, David J., Introduction to Electrodynamics (3rd ed.), Prentice Hall: pp. 386–389, 1998, ISBN 0-13-805326-X
4. ^ Moritz von Rohr p10
• 莫里兹·冯·罗尔《光学仪器成像的几何原理》Moritz von Rohr, Geometrical Investigation of the Formation of Images in Optical Instruments, H.M.STATIONARY OFFICE, LONDON, 1920