diff --git a/01.curriculum/01.physics-chemistry-biology/03.niv3/02.geometrical-optics/02.geometrical-optics-foundings/05.fermat-application/02.fermat-application-overview/cheatsheet.en.md b/01.curriculum/01.physics-chemistry-biology/03.niv3/02.geometrical-optics/02.geometrical-optics-foundings/05.fermat-application/02.fermat-application-overview/cheatsheet.en.md deleted file mode 100644 index f3190e2bd..000000000 --- a/01.curriculum/01.physics-chemistry-biology/03.niv3/02.geometrical-optics/02.geometrical-optics-foundings/05.fermat-application/02.fermat-application-overview/cheatsheet.en.md +++ /dev/null @@ -1,84 +0,0 @@ ---- -title: 'The 4 laws of geometrical optics' ---- - -* **Fermat's principle** *$\Longrightarrow$ the 4 laws of geometrical optics* : - -#### Law of reversibility of the path of light. - -Optical path and property of stationarity : concept of orientation not used
-*$\Longrightarrow$ stationarity property does not depend on the orientation* of the path. - -**$\Longrightarrow$** the **trajectory** *followed by the light* is **indépendant of the direction of propagation along the trajectory**. - -#### Law of the rectilinear light trajectory in homogeneous and isotrope media. - -Euclidian space : *straight line = shortest path between 2 points* - -**$\Longrightarrow$** in an **optically homogeneous and isotrope medium**, the *light travels rectilinearly* : the **light rays are straight lines**. - -#### The 2 laws of reflection and refraction -!
-! -! IF NECESSARY : reminder if the definitions of the angles and refractive indexes used below. -! -! $n_{incid}$ : refractive index of the incident light medium.
-! $n_{émerg}$ : refractive index of the emergent light medium (so after crossing the surface).
-! $i_{incid}$ : incident ray - normal to the surface at the point of impact angle.
-! $i_{émerg}$ : emergent ray - normal to the surface at the point of impact angle.
-!
- -For any incident ray impacting a surface : -* The **surface at the point of impact** is *locally a plane*. -* **Plan of incidence** : plane that *contains the incident ray and normal to the surface at the point of impact*. -* **Refracted and reflected rays** are *in the plane of incidence*, on the *side opposite to the incident ray in relation to the normal* at the surface at the impact point. - -*Reflection law* : **$i_{réflec} = i_{incid}$** - -*Refraction law (Snell-Descartes)* : for any $i_{incid}$ : -* if $\dfrac{n_{incid}}{n_{émerg}}\cdot\sin(i_{incid})\leqslant1$ then **refraction phenomenon** :

-**$n_{émerg}\cdot sin(i_{émerg})=n_{incid}\cdot sin(i_{incid})$**
- -* if $\dfrac{n_{incid}}{n_{emerg}}\cdot\sin(i_{incid})>1$ then **total reflection phenomenon** :
-*reflected ray* on the interface that follows the reflection law **$i_{réflec} = i_{incid}$**
- -* **Critical angle** (of inidence) **for total reflection : $i_{incid_limit}=\arcsin\left (\dfrac{n_{émerg}}{n_{incid}}\right)$** *$\Longrightarrow i_{émerg}=\pi/2\:rad = 90 °$* - -_Phenomena of reflection and refraction on a refracting surface._ - -![](interaction_lumiere_surface_3_650.gif) - -!!
-!! -!! TO GO FURTHER : intensity distribution between reflected and transmitted beam at a refracting surface. -!! -!! Geometrical optics: does not quantify the reflected $R$ and transmitted $T$ parts of the incident beam intensity at a plane refracting surface. This distribution varies according to the incidence angle, the polarization of the incident light, the wavelength. This is described by electromagnetism. -!! However a simple result is useful and to know : -!! *The light intensity is either reflected or transmitted* : $R+T=1$. -!! -!! For a light beam of wavelength $\lambda$ of normal incidence upon a refracting surface : -!! - ratio reflected power versus incident power : $R=\left(\dfrac{n_{incid}-n_{émerg}}{n_{incid}+n_{émerg}}\right)^2$ -!! - ratio transmitted power versus incident power : $T=1-R$ -!!
- -_Total reflection phenomenon_ - - - - - -![](Opt_Geo_refle_lim_650.gif) - - - - -