diff --git a/12.temporary_ins/65.geometrical-optics/50.simple-elements/30.thin-lens/20.overview/cheatsheet.en.md b/12.temporary_ins/65.geometrical-optics/50.simple-elements/30.thin-lens/20.overview/cheatsheet.en.md new file mode 100644 index 000000000..bc5961aa9 --- /dev/null +++ b/12.temporary_ins/65.geometrical-optics/50.simple-elements/30.thin-lens/20.overview/cheatsheet.en.md @@ -0,0 +1,161 @@ +--- +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 + +![](lens-convergent-N2-en.jpeg) + +* 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 + +![](lens-divergent-N2-en.jpeg) + +* 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.jpeg)
+_Converging thin lens representation : $\overline{OF}<0$ , $\overline{OF'}>0$ and $|\overline{OF}|=|\overline{OF'}|$_ + + ![](diverging-thin-lens-representation.jpeg)
+ _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** + +![](Const_lens_conv_point_AavantF.gif) + +* **Point source located between F et O** + +![](Const_lens_conv_point_AentreFO.gif) + +* **Virtual object point** (will be seen at level foothills, to remove from here). + +![](Const_lens_conv_point_AapresO.gif) + +##### Diverging thin lens + +(to be implemented)