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Update cheatsheet.en.md

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Claude Meny 6 years ago
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      01.curriculum/01.physics-chemistry-biology/03.Niv3/02.Geometrical-optics/02.geometrical-optics-foundings/01.concept-ray-of-light/02.concept-ray-of-light-overview/cheatsheet.en.md

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01.curriculum/01.physics-chemistry-biology/03.Niv3/02.Geometrical-optics/02.geometrical-optics-foundings/01.concept-ray-of-light/02.concept-ray-of-light-overview/cheatsheet.en.md

@ -53,7 +53,7 @@ I wanted to make this important remark here, but it is not simple: with Doppler
!! $`n`$: complex value dependent on the $\nu$ frequency of the electromagnetic wave, strong variations representative of all light / matter interaction mechanisms: $`n (\nu) = \Re[n(\nu )] + \Im[n(\nu)]`$ <br>
!!
!! on the visible domain (where $`\lambda_0`$ is more used than $`\nu`$) and for transparent medium : <br>
!! real value, small variations of $`n`$ with $`\lambda_0$ ($\frac{\Delta n}{n} <1 \%`$)
!! real value, small variations of $`n`$ with $`\lambda_0`$ ($`\frac{\Delta n}{n} <1 \%``$)
##### Optical path
@ -66,8 +66,8 @@ I wanted to make this important remark here, but it is not simple: with Doppler
* **$`\mathrm{d}\delta_P`$** : *infinitesimal optical path at point P on path $`\Gamma`$*
Optical path along a path between 2 fixed points A and B :
**$`\delta\;=\;\int_{P \in \Gamma}\mathrm{d}\delta_P\;=\;\int_{P \in \Gamma}n_P\cdot\mathrm{d}s_P`$**
**$`\delta\;=\;\displaystyle\int_{P \in \Gamma}\mathrm{d}\delta_P\;=\;\int_{P \in \Gamma}n_P\cdot\mathrm{d}s_P`$**
* **$`\delta`$** $`=\displaystyle\int_{\Gamma}n\cdot\mathrm{d}s\;=\;\int_{\Gamma}\frac{c}{v}\cdot\mathrm{d}s`$ = $`c\;\int_{\Gamma}\frac{\mathrm{d}s}{v}`$ = *$`\;c\;\tau`$*
* **$`\delta`$** $`=\displaystyle\int_{\Gamma}n\cdot\mathrm{d}s\;=\;\int_{\Gamma}\dfrac{c}{v}\cdot\mathrm{d}s`$ = $`c\;\displaystyle\int_{\Gamma}\dfrac{\mathrm{d}s}{v}`$ = *$`\;c\;\tau`$*
* **$`\delta`$** is *proportional to the travel time*.
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