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Display information for equation id:math.2164.20 on revision:2164

* Page found: Brechung und Reflexion (eq math.2164.20)

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Hash: 8bc615ae3f448eb47b1e1b2fe42d49ad

TeX (original user input): 

\begin{align}
& {{k}_{3}}\acute{\ }\acute{\ }=\left| \bar{k}\acute{\ }\acute{\ } \right|\cos \gamma \acute{\ }\acute{\ }=\left| \bar{k}\acute{\ } \right|\frac{{{n}_{2}}}{{{n}_{1}}}\cos \gamma \acute{\ }\acute{\ } \\
& \frac{{{n}_{2}}}{{{n}_{1}}}=\frac{\sin \gamma }{\sin \gamma \acute{\ }\acute{\ }} \\
& \Rightarrow {{k}_{3}}\acute{\ }\acute{\ }=\left| \bar{k}\acute{\ }\acute{\ } \right|\cos \gamma \acute{\ }\acute{\ }=\left| \bar{k}\acute{\ } \right|\frac{\sin \gamma }{\sin \gamma \acute{\ }\acute{\ }}\cos \gamma \acute{\ }\acute{\ } \\
& {{k}_{3}}=\left| {\bar{k}} \right|\cos \gamma  \\
\end{align}

TeX (checked): 

{\begin{aligned}&{{k}_{3}}{\acute {\ }}{\acute {\ }}=\left|{\bar {k}}{\acute {\ }}{\acute {\ }}\right|\cos \gamma {\acute {\ }}{\acute {\ }}=\left|{\bar {k}}{\acute {\ }}\right|{\frac {{n}_{2}}{{n}_{1}}}\cos \gamma {\acute {\ }}{\acute {\ }}\\&{\frac {{n}_{2}}{{n}_{1}}}={\frac {\sin \gamma }{\sin \gamma {\acute {\ }}{\acute {\ }}}}\\&\Rightarrow {{k}_{3}}{\acute {\ }}{\acute {\ }}=\left|{\bar {k}}{\acute {\ }}{\acute {\ }}\right|\cos \gamma {\acute {\ }}{\acute {\ }}=\left|{\bar {k}}{\acute {\ }}\right|{\frac {\sin \gamma }{\sin \gamma {\acute {\ }}{\acute {\ }}}}\cos \gamma {\acute {\ }}{\acute {\ }}\\&{{k}_{3}}=\left|{\bar {k}}\right|\cos \gamma \\\end{aligned}}

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MathML (46.692 KB / 4.629 KB) :

k 3 ⁢ ´ ⁢ ´ = | k ¯ ⁢ ´ ⁢ ´ | ⁢ cos ⁡ γ ⁢ ´ ⁢ ´ = | k ¯ ⁢ ´ | ⁢ n 2 n 1 ⁢ cos ⁡ γ ⁢ ´ ⁢ ´ n 2 n 1 = sin ⁡ γ sin ⁡ γ ⁢ ´ ⁢ ´ ⇒ k 3 ⁢ ´ ⁢ ´ = | k ¯ ⁢ ´ ⁢ ´ | ⁢ cos ⁡ γ ⁢ ´ ⁢ ´ = | k ¯ ⁢ ´ | ⁢ sin ⁡ γ sin ⁡ γ ⁢ ´ ⁢ ´ ⁢ cos ⁡ γ ⁢ ´ ⁢ ´ k 3 = | k ¯ | ⁢ cos ⁡ γ missing-subexpression subscript 𝑘 3 ´ absent ´ absent ¯ 𝑘 ´ absent ´ absent 𝛾 ´ absent ´ absent ¯ 𝑘 ´ absent subscript 𝑛 2 subscript 𝑛 1 𝛾 ´ absent ´ absent missing-subexpression subscript 𝑛 2 subscript 𝑛 1 𝛾 𝛾 ´ absent ´ absent missing-subexpression ⇒ absent subscript 𝑘 3 ´ absent ´ absent ¯ 𝑘 ´ absent ´ absent 𝛾 ´ absent ´ absent ¯ 𝑘 ´ absent 𝛾 𝛾 ´ absent ´ absent 𝛾 ´ absent ´ absent missing-subexpression subscript 𝑘 3 ¯ 𝑘 𝛾 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle{{k}_{3}}\acute{\ }% \acute{\ }=\left|\bar{k}\acute{\ }\acute{\ }\right|\cos\gamma\acute{\ }\acute{% \ }=\left|\bar{k}\acute{\ }\right|\frac{{{n}_{2}}}{{{n}_{1}}}\cos\gamma\acute{% \ }\acute{\ }\\ &\displaystyle\frac{{{n}_{2}}}{{{n}_{1}}}=\frac{\sin\gamma}{\sin\gamma\acute{% \ }\acute{\ }}\\ &\displaystyle\Rightarrow{{k}_{3}}\acute{\ }\acute{\ }=\left|\bar{k}\acute{\ }% \acute{\ }\right|\cos\gamma\acute{\ }\acute{\ }=\left|\bar{k}\acute{\ }\right|% \frac{\sin\gamma}{\sin\gamma\acute{\ }\acute{\ }}\cos\gamma\acute{\ }\acute{\ % }\\ &\displaystyle{{k}_{3}}=\left|{\bar{k}}\right|\cos\gamma\\ \end{aligned}}}

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MathML (6.478 KB / 515 B) :

k3´´=|k¯´´|cos⁡γ´´=|k¯´|n2n1cos⁡γ´´n2n1=sin⁡γsin⁡γ´´⇒k3´´=|k¯´´|cos⁡γ´´=|k¯´|sin⁡γsin⁡γ´´cos⁡γ´´k3=|k¯|cos⁡γ

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