Lindsey Yue edited section_Generalized_Snell_s_Law__.tex  almost 8 years ago

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w'_{\mathrm{t}} w''_{\mathrm{t}} = \eta_{0}^{2} \left( n_{2} k_{2} \right)  \end{equation}  %  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  %  \begin{equation}  w_{\mathrm{i}}' = \eta_{0} n_{1}  \end{equation}  %  \begin{equation}  w_{\mathrm{i}}'' = 0  \end{equation}