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Feb 09, 20251 min read

Boundary conditions for light going through different media

$ε_{1} E_{1}^{⊥} = ε_{2} E_{2}^{⊥}$

$\displaystyle {\varepsilon}_{1}E_{1}^{\perp}={\varepsilon}_{2}E_{2}^{\perp}$
$\displaystyle B_{1}^{\perp}=B_{2}^{\perp}$
$\displaystyle \vec{E}_{1}^{\parallel }=\vec{E}_{2}^{\parallel }$
$\displaystyle \frac{1}{{\mu}_{1}}\vec{B}_{1}^{\parallel }-\frac{1}{{\mu}_{2}}\vec{B}^{\parallel }=\vec{K}_{f}\times \hat{n}$