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\begin{document}
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{\large{Fresnelovy amplitudy}}\\

$\bullet$ Pro odražené světlo\\
\begin{equation}
r_{\rm{p}} = \frac{n_{2}\cos \varphi_{1} - n_{1}\cos \varphi_{2}}{n_{2}\cos \varphi_{1} + n_{1}\cos \varphi_{2}}
\nonumber 
\end{equation}

\begin{equation}
r_{\rm{s}} = \frac{n_{1}\cos \varphi_{1} - n_{2}\cos \varphi_{2}}{n_{1}\cos \varphi_{1} + n_{2}\cos \varphi_{2}}
\nonumber 
\end{equation}

$\bullet$ Pro lomené světlo\\
\begin{equation}
t_{\rm{p}} = \frac{2 n_{1}\cos \varphi_{1}}{n_{2}\cos \varphi_{1} + n_{1}\cos \varphi_{2}}
\nonumber 
\end{equation}

\begin{equation}
t_{\rm{s}} = \frac{2 n_{1}\cos \varphi_{1}}{n_{1}\cos \varphi_{1} + n_{2}\cos \varphi_{2}}
\nonumber 
\end{equation}

Odraznost\\
\begin{equation}
R_{\rm{p}} = r_{\rm{p}}^{2}
\nonumber 
\end{equation}

\begin{equation}
R_{\rm{s}} = r_{\rm{s}}^{2}
\nonumber 
\end{equation}

\begin{equation}
2R = R_{\rm{p}} + R_{\rm{s}}
\nonumber 
\end{equation}

Propustnost\\
\begin{equation}
T_{\rm{p}} = \frac{n_{2} \cos \varphi_{2}}{n_{1} \cos \varphi_{1}} \, t_{\rm{p}}^{2}
\nonumber 
\end{equation}

\begin{equation}
T_{\rm{s}} = \frac{n_{2} \cos \varphi_{2}}{n_{1} \cos \varphi_{1}} \, t_{\rm{s}}^{2}
\nonumber 
\end{equation}

\begin{equation}
2T = T_{\rm{p}} + T_{\rm{s}}
\nonumber 
\end{equation}

Snellův zákon lomu\\
\begin{equation}
\varphi_{2} = \arcsin \left( \sin \varphi_{1} \, \frac{n_{2}}{n_{1}} \right)
\nonumber 
\end{equation}

\vspace{15pt}

{\noindent
$p$ - v rovině dopadu\\
$s$ - kolmo k rovině dopadu\\
$\varphi_{1}$ - úhel dopadu\\
$\varphi_{2}$ - úhel lomu
}

\vspace{15pt}

\begin{equation}
R = \frac{1}{2} \left[ { \left( \frac{n_{2}\cos \varphi_{1} - n_{1}\cos \varphi_{2}}{n_{2}\cos \varphi_{1} + n_{1}\cos \varphi_{2}}\right)}^{2} + { \left( \frac{n_{1}\cos \varphi_{1} - n_{2}\cos \varphi_{2}}{n_{1}\cos \varphi_{1} + n_{2}\cos \varphi_{2}}\right)}^{2} \right]
\nonumber 
\end{equation}

\begin{equation}
T =  \frac{1}{2} \, \frac{n_{2} \cos \varphi_{2}}{n_{1} \cos \varphi_{1}} \, \left[ { { \left( { \frac{2 n_{1}\cos \varphi_{1}}{n_{2}\cos \varphi_{1} + n_{1}\cos \varphi_{2}}} \right) }^{2} + {  \left( \frac{2 n_{1}\cos \varphi_{1}}{n_{1}\cos \varphi_{1} + n_{2}\cos \varphi_{2}} \right) }^{2} } \right]
\nonumber 
\end{equation}

\begin{equation}
\cos \varphi_{2} = \sqrt{ 1 - { \left( \sin \varphi_{1} \, \frac{n_{2}}{n_{1}} \right) }^{2}}
\nonumber 
\end{equation}

\begin{equation}
1 = R + T
\nonumber 
\end{equation}



\end{document}

