4.2 KiB
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| 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
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! 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 $i_{incid}$ :
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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.
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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 : $T=1-R$ !!Total reflection phenomenon
smartphone : switch to "landscape" mode to see the geogebra animations.
