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16112.temporary_ins/65.geometrical-optics/50.simple-elements/30.thin-lens/20.overview/cheatsheet.en.md
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title: 'The thin lens' |
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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' |
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published: true |
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routable: true |
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visible: false |
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lessons: |
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- slug: simple-optical-elements |
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- order: 3 |
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--- |
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!!!! *COURS EN CONSTRUCTION :* <br> |
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!!!! 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> |
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!!!! Document de travail destiné uniquement aux équipes pédagogiques. |
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<!--MétaDonnée : ... --> |
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-------------------- |
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### What is a lens ? |
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#### Objective |
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* initial : to **focuse or disperse the light**. |
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* ultimate : to **realize images**, alone or as part of optical instruments. |
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#### Physical principle |
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* **uses the refractive phenomenon**, described by the Snell-Descartes' law. |
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#### Constitution |
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* Piece of **glass, quartz, plastic** (for visible and near infrared and UV). |
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* **Rotationally symmetrical**. |
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* **2 polished surfaces** perpendicular to its axis of symmetry, **either or both curved** (and most often spherical). |
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<!--image to build : a thin lens--> |
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#### Interest in optics : thin lenses |
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* **Thin lens** : *thickness << diameter* |
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* 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. |
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<!--image to build N1 ou N2 : a composition : |
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upper medium : a unic thin lens |
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upper part towards utilization of a unique lens : magnigfying glass and eyeglasses |
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lower medium : small serie of centered naked lenses |
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lower part toward utilization of combined lenses : macroscope, camera (apparatus and objective of a cellular), refracting telescope, teleopbjective--> |
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### Modeling a thin lens surrounded by air, gaz or vaccum. |
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#### Why modeling ? |
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* To **understand, calculate and predict images** of objects given by thin lenses |
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<!--picture when we see the object, the lens and the image--> |
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##### Why surrounded by air, gaz or vaccum? |
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* **In most optical instruments**, lenses are *surrounding by air*. |
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* **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> |
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$\Longrightarrow$ same optical behavior in air, gaz and vacuum. |
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#### Types and characterization of thin lenses |
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**Convergent** = **converging** = **convexe** = **positive** lenses |
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* Characterized by :<br> |
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\- **Focal lenght** (usually in cm) always >0 *+* adjective "**converging**"<br> |
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or<br> |
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\- Its **image focal length** $f'$ (in *algebraic value*, usually in cm), that is *positive $f'>0$*.<br> |
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or<br> |
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\- Its **vergence** $V$ (in ophtalmology) that is *positive $V>0$*,<br> |
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with $V (\delta)=\dfrac{1}{f'(m)}$ ($f'$ being expresssed in m "meter" and $V$ in $\delta$ "dioptre", so $\delta=m^{-1}$).<br> |
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**Divergent** = **diverging** = **concave ** = **negative** lenses |
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* Characterized by :<br> |
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\- **Focal lenght** (usually in cm) always >0 *+* adjective "**diverging**"<br> |
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or<br> |
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\- Its **image focal length** $f'$ (in *algebraic value*, usually in cm), that is *negative $f'<0$*.<br> |
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or<br> |
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\- Its **vergence** $V$ (in ophtalmology) that is *negative $V<0$*,<br> |
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with $V (\delta)=\dfrac{1}{f'(m)}$ ($f'$ being expresssed in m "meter" and $V$ in $\delta$ "dioptre", so $\delta=m^{-1}$).<br> |
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<!-- suppressed |
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#### What physical framework, model and technics ? |
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* _Framework : Geometrical Optics = Light rays optics $\longrightarrow$ foothills stage_. |
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* _Model : paraxial model = gaussian model $\longrightarrow$ foothills stage_. |
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* Model splits in *two different technics (but equivalent)* :<br> **graphical modeling** AND **analytical modeling** |
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* *Differences between model predictions and experimental observations* : ** optical aberrations** (_under control, minimized and negligeable in optical instruments_). |
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--> |
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### Analytical modeling |
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(_for thin lens surrounded by air, gaz or vaccum_) |
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##### Thin lens equation |
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**$\dfrac{1}{\overline{OA'}}-\dfrac{1}{\overline{OA}}=V=-\dfrac{1}{\overline{OF}}=\dfrac{1}{\overline{OF'}}$** |
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##### Transverse magnification expression |
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**$M_{T-thinlens}=\dfrac{\overline{OA'}}{\overline{OA}}$** |
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### Graphical modeling |
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#### Thin lens representation |
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* **optical axis** = *revolution axis* of the lens, positively *oriented* in the direction of propagation of the light (_from the object towards the lens_). |
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* **thins lens representation** :<br><br> |
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\- *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> |
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\- **S = C = O** : vertex S = nodal point C = center O of the thin lens $\Longrightarrow$ is used point O.<br><br> |
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\- *point O*, intersection of the line segment with optical axis.<br><br> |
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\- *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> |
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\- *object focal plane (P)* and *image focal plane (P')*, planes perpendicular to the optical axis at respectively points $F$ and $F'$. |
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<br> |
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_Converging thin lens representation : $\overline{OF}<0$ , $\overline{OF'}>0$ and $|\overline{OF}|=|\overline{OF'}|$_ |
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<br> |
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_Divverging thin lens representation : $\overline{OF}>0$ , $\overline{OF'}<0$ and $|\overline{OF}|=|\overline{OF'}|$_ |
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#### Determining conjugate points : |
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##### Converging thin lens |
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<!-- |
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**Towards geogebra animations** :<br> |
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\- Graphical construction<br> |
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[Click here for geogebra animation](https://www.geogebra.org/material/iframe/id/zqwazusz)<br> |
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\- Graphical construction and light pencils <br> |
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[Click here for geogebra animation](https://www.geogebra.org/material/iframe/id/wkrw5qgm)<br> |
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\- Graphical construction and transverse magnification<br> |
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[Click here for geogebra animation](https://www.geogebra.org/material/iframe/id/xwbwedft)<br> |
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--> |
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* **Point source located between ∞ et F** |
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* **Point source located between F et O** |
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* **Virtual object point** (will be seen at level foothills, to remove from here). |
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##### Diverging thin lens |
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(to be implemented) |
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