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Lindsey Yue edited section_Generalized_Snell_s_Law__.tex
almost 8 years ago
Commit id: af0d837d300924971be0a8625d9c20940d87e472
deletions | additions
diff --git a/section_Generalized_Snell_s_Law__.tex b/section_Generalized_Snell_s_Law__.tex
index 3e465e9..d00bed9 100644
--- a/section_Generalized_Snell_s_Law__.tex
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w'_{\mathrm{t}} w''_{\mathrm{t}} = \eta_{0}^{2} \left( n_{2} k_{2} \right)
\end{equation}
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Equations \ref{eq:1}, \ref{eq:2}, \ref{eq:3}, \ref{eq:4}, and \ref{eq:5} constitute a system of five equations with the following five unknowns: $\theta_{2}, w_{\mathrm{i}}', w_{\mathrm{i}}'', w_{\mathrm{t}}', w_{\mathrm{t}}''$. $\theta_{2}$ can therefore be solved for in terms of $m_{1}$ and $m_{2}$.
If the algebra for that proves too complicated, the equations can be simplifed if medium 2 is assumed to be non-absorbing. Equations \ref{eq:4} and \ref{eq:5} reduce to
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\begin{equation}
w_{\mathrm{i}}' = \eta_{0} n_{1}
\end{equation}
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\begin{equation}
w_{\mathrm{i}}'' = 0
\end{equation}