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-title: 'The 4 laws of geometrical optics'
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-* **Fermat's principle** *$\Longrightarrow$ the 4 laws of geometrical optics* :
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-#### Law of reversibility of the path of light.
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-Optical path and property of stationarity : concept of orientation not used
-*$\Longrightarrow$ stationarity property does not depend on the orientation* of the path.
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-**$\Longrightarrow$** the **trajectory** *followed by the light* is **indépendant of the direction of propagation along the trajectory**.
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-#### Law of the rectilinear light trajectory in homogeneous and isotrope media.
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-Euclidian space : *straight line = shortest path between 2 points*
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-**$\Longrightarrow$** in an **optically homogeneous and isotrope medium**, the *light travels rectilinearly* : the **light rays are straight lines**.
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-#### 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.
-!
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-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.
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-*Reflection law* : **$i_{réflec} = i_{incid}$**
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-*Refraction law (Snell-Descartes)* : for any $i_{incid}$ :
-* if $\dfrac{n_{incid}}{n_{émerg}}\cdot\sin(i_{incid})\leqslant1$ then **refraction phenomenon** :
-**$n_{émerg}\cdot sin(i_{émerg})=n_{incid}\cdot sin(i_{incid})$**
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-* 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 **$i_{réflec} = i_{incid}$**
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-* **Critical angle** (of inidence) **for total reflection : $i_{incid_limit}=\arcsin\left (\dfrac{n_{émerg}}{n_{incid}}\right)$** *$\Longrightarrow i_{émerg}=\pi/2\:rad = 90 °$*
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-_Phenomena of reflection and refraction on a refracting surface._
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-!!
-!!
-!! 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 : $T=1-R$
-!!
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-_Total reflection phenomenon_
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