!!!! Publié mais invisible : n'apparait pas dans l'arborescence du site m3p2.com. Ce cours est *en construction*, il n'est *pas validé par l'équipe pédagogique* à ce stade. <br>
!!!! Document de travail destiné uniquement aux équipes pédagogiques.
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### What is a lens ?
#### Objective
* initial : to **focuse or disperse the light**.
* ultimate : to **realize images**, alone or as part of optical instruments.
#### Physical principle
***uses the refractive phenomenon**, described by the Snell-Descartes' law.
#### Constitution
* Piece of **glass, quartz, plastic** (for visible and near infrared and UV).
***Rotationally symmetrical**.
***2 polished surfaces** perpendicular to its axis of symmetry, **either or both curved** (and most often spherical).
<!--image to build : a thin lens-->
#### Interest in optics : thin lenses
***Thin lens** : *thickness << diameter*
* Thins lens : **most important simple optical element** that is *used alone or combined in serie in most optical instruments* : magnifying glasses, microscopes, tele and macro objectives, camera, refracting telescopes.
<!--image to build N1 ou N2 : a composition :
upper medium : a unic thin lens
upper part towards utilization of a unique lens : magnigfying glass and eyeglasses
lower medium : small serie of centered naked lenses
lower part toward utilization of combined lenses : macroscope, camera (apparatus and objective of a cellular), refracting telescope, teleopbjective-->
### Modeling a thin lens surrounded by air, gaz or vaccum.
#### Why modeling ?
* To **understand, calculate and predict images** of objects given by thin lenses
<!--picture when we see the object, the lens and the image-->
##### Why surrounded by air, gaz or vaccum?
***In most optical instruments**, lenses are *surrounding by air*.
***air, gaz and vaccum** have refractive index values in the range "$1.000\pm0.001$, and can be approximated by *$n_{air}=n_{gaz}=n_{vaccum}=1$*<br>
$\Longrightarrow$ same optical behavior in air, gaz and vacuum.
* _Model : paraxial model = gaussian model $\longrightarrow$ foothills stage_.
* Model splits in *two different technics (but equivalent)* :<br>**graphical modeling** AND **analytical modeling**
**Differences between model predictions and experimental observations* : ** optical aberrations** (_under control, minimized and negligeable in optical instruments_).
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### Analytical modeling
(_for thin lens surrounded by air, gaz or vaccum_)
***optical axis** = *revolution axis* of the lens, positively *oriented* in the direction of propagation of the light (_from the object towards the lens_).
***thins lens representation** :<br><br>
\-*line segment*, perpendicular to optical axis, centered on the axis with symbolic *indication of the lens shape* at its extremities (_convexe or concave_).<br><br>
\-**S = C = O** : vertex S = nodal point C = center O of the thin lens $\Longrightarrow$ is used point O.<br><br>
\-*point O*, intersection of the line segment with optical axis.<br><br>
\-*object focal point F* and *image focal point F'*, positioned on the optical axis symmetrically with respect to the point O ($f=-f'$) at algebraic distances $\overline{OF}=f$ and $\overline{OF'}=f'$.<br><br>
\-*object focal plane (P)* and *image focal plane (P')*, planes perpendicular to the optical axis at respectively points $F$ and $F'$.
<br>
_Converging thin lens representation : $\overline{OF}<0$ , $\overline{OF'}>0$ and $|\overline{OF}|=|\overline{OF'}|$_
<br>
_Divverging thin lens representation : $\overline{OF}>0$ , $\overline{OF'}<0$ and $|\overline{OF}|=|\overline{OF'}|$_
#### Determining conjugate points :
##### Converging thin lens
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**Towards geogebra animations** :<br>
\- Graphical construction<br>
[Click here for geogebra animation](https://www.geogebra.org/material/iframe/id/zqwazusz)<br>
\- Graphical construction and light pencils <br>
[Click here for geogebra animation](https://www.geogebra.org/material/iframe/id/wkrw5qgm)<br>
\- Graphical construction and transverse magnification<br>
[Click here for geogebra animation](https://www.geogebra.org/material/iframe/id/xwbwedft)<br>
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***Point source located between ∞ et F**
***Point source located between F et O**
***Virtual object point** (will be seen at level foothills, to remove from here).
