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Display information for equation id:math.3834.2 on revision:3834
* Page found: Brechungsindizes (eq math.3834.2)
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Hash: 50fa8fc54464aebbcb68f5720c5fc0fe
TeX (original user input):
\frac{\sin \alpha _1 }{\sin\alpha_2}=\frac{n_2}{n_1}\Rightarrow \alpha_c = \sin^{-1}(1-\delta)\approx \frac\pi2-\sqrt{2\delta}
TeX (checked):
{\frac {\sin \alpha _{1}}{\sin \alpha _{2}}}={\frac {n_{2}}{n_{1}}}\Rightarrow \alpha _{c}=\sin ^{-1}(1-\delta )\approx {\frac {\pi }{2}}-{\sqrt {2\delta }}
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MathML (1.455 KB / 341 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>sin</mi><mo>⁡</mo><msub><mi>α</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>sin</mi><mo>⁡</mo><msub><mi>α</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mrow></mfrac></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mfrac></mrow><mo>⇒</mo><msub><mi>α</mi><mrow data-mjx-texclass="ORD"><mi>c</mi></mrow></msub><mo>=</mo><msup><mi>sin</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mn>1</mn></mrow></mrow></msup><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>δ</mi><mo stretchy="false">)</mo><mo>≈</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>π</mi></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo>−</mo><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>δ</mi></mrow></msqrt></mrow></mstyle></mrow></math>
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