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----
-title: 'The thin lens'
-media_order: 'Const_lens_conv_point_AapresO.gif,lens-convergent-N2-en.jpeg,Const_lens_conv_point_AentreFO.gif,lens-convergent-N2-es.jpeg,lens-convergent-N2-fr.jpeg,Const_lens_conv_point_AavantF.gif,lens-divergent-N2-es.jpeg,lens-divergent-N2-fr.jpeg,lens-divergent-N2-en.jpeg,diverging-thin-lens-representation.jpeg,converging-thin-lens-representation.jpeg'
-published: true
-routable: true
-visible: false
-lessons:
- - slug: simple-optical-elements
- - order: 3
----
-
-!!!! *COURS EN CONSTRUCTION :*
-!!!! 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.
-!!!! Document de travail destiné uniquement aux équipes pédagogiques.
-
-
-
-
---------------------
-
-### 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).
-
-
-
-#### 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.
-
-
-
-### Modeling a thin lens surrounded by air, gaz or vaccum.
-
-#### Why modeling ?
-
-* To **understand, calculate and predict images** of objects given by thin lenses
-
-
-
-##### 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 *$n_{air}=n_{gaz}=n_{vaccum}=1$*
-$\Longrightarrow$ same optical behavior in air, gaz and vacuum.
-
-#### Types and characterization of thin lenses
-
-**Convergent** = **converging** = **convexe** = **positive** lenses
-
-
-
-* Characterized by :
-\- **Focal lenght** (usually in cm) always >0 *+* adjective "**converging**"
- or
-\- Its **image focal length** $f'$ (in *algebraic value*, usually in cm), that is *positive $f'>0$*.
- or
-\- Its **vergence** $V$ (in ophtalmology) that is *positive $V>0$*,
-with $V (\delta)=\dfrac{1}{f'(m)}$ ($f'$ being expresssed in m "meter" and $V$ in $\delta$ "dioptre", so $\delta=m^{-1}$).
-
-**Divergent** = **diverging** = **concave ** = **negative** lenses
-
-
-
-* Characterized by :
-\- **Focal lenght** (usually in cm) always >0 *+* adjective "**diverging**"
- or
-\- Its **image focal length** $f'$ (in *algebraic value*, usually in cm), that is *negative $f'<0$*.
- or
-\- Its **vergence** $V$ (in ophtalmology) that is *negative $V<0$*,
-with $V (\delta)=\dfrac{1}{f'(m)}$ ($f'$ being expresssed in m "meter" and $V$ in $\delta$ "dioptre", so $\delta=m^{-1}$).
-
-
-
-### Analytical modeling
-
-(_for thin lens surrounded by air, gaz or vaccum_)
-
-##### Thin lens equation
-**$\dfrac{1}{\overline{OA'}}-\dfrac{1}{\overline{OA}}=V=-\dfrac{1}{\overline{OF}}=\dfrac{1}{\overline{OF'}}$**
-
-##### Transverse magnification expression
-**$M_{T-thinlens}=\dfrac{\overline{OA'}}{\overline{OA}}$**
-
-
-### Graphical modeling
-
-#### Thin lens representation
-
-* **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** :
-\- *line segment*, perpendicular to optical axis, centered on the axis with symbolic *indication of the lens shape* at its extremities (_convexe or concave_).
-\- **S = C = O** : vertex S = nodal point C = center O of the thin lens $\Longrightarrow$ is used point O.
-\- *point O*, intersection of the line segment with optical axis.
-\- *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 $\overline{OF'}=f'$.
-\- *object focal plane (P)* and *image focal plane (P')*, planes perpendicular to the optical axis at respectively points $F$ and $F'$.
-
-
-_Converging thin lens representation : $\overline{OF}<0$ , $\overline{OF'}>0$ and $|\overline{OF}|=|\overline{OF'}|$_
-
- 
- _Divverging thin lens representation : $\overline{OF}>0$ , $\overline{OF'}<0$ and $|\overline{OF}|=|\overline{OF'}|$_
-
-#### Determining conjugate points :
-
-##### Converging thin lens
-
-
-
-* **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).
-
-
-
-##### Diverging thin lens
-
-(to be implemented)