a first and odl step, TO REWRITE COMPLETELY

01.curriculum/01.physics-chemistry-biology/03.Niv3/02.Geometrical-optics/05.paraxial-optics/02.paraxial-optics-simple-elements/03.lens/02.lens-overview/cheatsheet.en.md

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-title : "towards thin lens overview"
+title : lens-overview
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+media_order: 'lens-convergent-N3-en.jpeg,lens-divergent-N3-en.jpeg,Const_lens_conv_point_AavantF2.gif,thick-lens-water-air.gif,Lentille_epaisse_Gauss_incl_v1.gif,2-centered-refracting-surfaces-1-all.gif,2-refracting-surface-physical-system.jpeg,2-centered-refracting-surfaces-direction-axis.gif,Lentille_epaisse_principe_ok.gif,lentille_relle_representation_v1.gif,Const_lens_conv_point_AapresO.gif,lens-convergent-N3-es.jpeg,lens-convergent-N3-fr.jpeg,lens-divergent-N3-es.jpeg,lens-divergent-N3-fr.jpeg'
+---
+TO REWRITE COMPLETELY
+
+
+### Two successive and centered spherical refracting surfaces
+
+!!! *WHERE YOU ARE* :<br>
+!!! Observation $`\Rightarrow`$ Geometrical optic interpretation $`\Rightarrow`$ Fermat's Principle $`\Rightarrow`$ 
+The 5 optical laws $`\Rightarrow`$ Paraxial approximation $`\Rightarrow`$ Simple optical element $`\Rightarrow`$ System 
+of 2 simple optical elements.
+
+! *THIS CHAPTER AIMS AT* :
+! * Deeply understand and better master thin lenses.<br>
+! * Understand when the lens equation and the coresponding transverse magnification expression can be used, and when they are not correct.
+!  * Understand need and requirement of new concepts to master esaily and efficientlynext main chapter "Centered optical systems".
+
+*Two successive and centered spherical refracting surfaces* = **thick lens**
+
+##### Thick lens as a physical system
+
+**Physical system** =  *spatial distribution of the refracting indexes values* (_variations of refracting index can 
+be discontinuous with interfaces (_refracting surfaces, lenses, mirrors_) or continuous (graded-index optical fiber)_.
+
+**Optical system** = *oriented physical system* = *physical systems + bodies (1) + a direction (2)* <br>
+* (1) : which emit, diffuse or reflect the ambiant light.
+* (2) : direction of light propagation considered through the physical system. 
+
+**Difference** between physical and optical system in optics :
+
+Example of the lensball :
+Physical system of a lensball :
+
+**Thick lens** physical system :<br>
+Most general : *3 different transparent media with their own refractive index values*, and *2 local spherical interfaces* 
+that separate these media, and *centered on the straigth line* that joins their centers of curvature._
+
+**Examples** in images :
+
+![](2-refracting-surface-physical-system.jpeg)
+
+##### Thick lens as an optical system
+
+**Optical system** = *oriented physical system* = *physical systems + bodies (1) + a direction (2)* 
+
+* (1) : which emit, diffuse or reflec the ambiant light
+* (2) : direction of light propagation considered through the two refracting surfaces. 
+
+*From physical system to optical system* : **a scenario to build** :
+* Where is the object that is imaged ?
+* In what direction are we searching for images ?
+* what are the reflecting or refracting interfaces we take into account.
+
+<!--To define an optical system, you have to find a scenario : where is the objet to be imaged or viewed ?
+And where is the real image of the object to be registered by a matrix sensor or where is located the eye of
+the observator ? This gives you the direction of propagation (from object to real image or eye) through the optical
+system. This direction of propagation is part of the description of the optical system. In the figure above the optical
+systems are each time two ordered spherical refracting surfaces._-->
+
+
+_The physical system consists of two bubble aquariums side by side. In each of them, a fish, and the two fish, Jones and 
+Tessa face each other. These two situations correspond to two optical systems: "Tessa looks at Jones" and "Jones looks at Tessa"
+(the order of crossing of the refracting surfaces by the light is reversed in both cases). In the situtation we want to describe, 
+the direction of the light is indicated (the brown arrow in the figures)_
+
+**Graphical representation** (drawing) and **analytical representation** (*3 algebraic distances* : 2 radius of curvature
+$`\overline{S_1C_1}`$, $`\overline{S_2C_2}`$,+ distance between the two vertices of the refracting surfaces $`\overline{S_1S_2}`$ 
+*when used in the paraxial (or same, gaussian) approximation, so when considered in paraxial optics.
+
+_ In order to identify conjugated points, to construct the final image of a specific object for example, the optical axis 
+of the optical system is plotted, vertices and centers of curvature of spherical refracting surfaces are localised on the optica
+l axis. Because 
+
+
+
+!!! Thick lens
+
+
+
+
+![](thick-lens-water-air.gif)
+
+![](2-centered-refracting-surfaces-1-all.gif)
+
+![](2-centered-refracting-surfaces-direction-axis.gif)
+
+![](thick-lens-water-air.gif)
+
+![](Const_lens_conv_point_AapresO.gif)
+
+![](Const_lens_conv_point_AavantF2.gif)
+
+![](Lentille_epaisse_Gauss_incl_v1.gif)
+
+![](thick-lens-water-air.gif)
+
+![](Lentille_epaisse_principe_ok.gif)
+
+![](lentille_relle_representation_v1.gif)
+
+
+### The thin lens
+
+##### Objective
+to **focuse or disperse the light**,<br> 
+with often the final goal, alone or as part of optical instruments, to **realize images**.
+
+##### Physical principle
+**uses the refractive phenomenon**, described by the Snell-Descartes' law.
+
+##### Characterization of its efficiency
+(efficiency to realize its objective)
+
+**Vergence** = **dioptric power** V of the lens :
+
+* **unit** : in S.I. : the *diopter*, of symbol $`\delta`$<br>
+ 1 diopter = 1 $`\delta`$ = 1 $`m^{-1}`$).
+* **positive vergence** ($`V>0)\:\Longleftrightarrow`$ *light focalisation : convergent lens*.<br>
+* **negative vergence** ($`V<0)\:\Longleftrightarrow`$ *light dispersion : divergent lens*.<br>
+* **absolute value** of the vergence ($`|V|`$) : *increases as the optical phenomenon (focalisation or dispersion) increases*
+* (as the corresponding deviation of light rays increases).<br>
+* **interest** : The *total vergence* of several __contiguous thin lenses__ is the *sum of the vergences of each of the lenses* : $`V=\sum V_i`$.
+
+or (equivalent)
+
+**image focal length** $`f'`$ of the lens : 
+
+* **positive $`f'`$** ($`f'>0)\:\Longleftrightarrow`$ *focuses light : convergent lens*<br>
+* **negative $`f'`$** ($`f'<0)\:\Longleftrightarrow`$ *disperse light : divergent lens*<br>
+* **absolute value of $`f'`$** ($`|f'|`$) : *decreases as the optical phenomenon (focalisation or dispersion) increases*.<br>
+* **interest** : For thin lenses, the **algebraic value of $f'$** give the *position of the plane* (perpendicular to 
+* the optical axis) and from the lens center *where the image of an object at infinity takes place*. 
+
+! Nearby in all application, same medium (same refractive index) in both sides of the lens :<br>
+! $`\Longrightarrow`$ object focal lenght $`f`$ is the opposite of image focal length $`f'`$ : $`f=-f'`$<br>
+! $`\Longrightarrow`$ only absolute value $`|f'|`$ of $`f'`$ is given, and the lens is specified to be convergeng or divergent.
+
+**Relation between vergence (dioptric power), image and object focal lengthes**
+
+if the refractive index $`n_{ini}`$ of the medium in which the incident light on the lens propagates, and $`n_{fin}`$ of the medium 
+in which the light emerges from the lens, then :
+
+$`V=-\dfrac{n_{ini}}{f}=+\dfrac{n_{fin}}{f'}`$
+
+##### Constitution
+
+Piece of **glass, quartz, plastic** (for visible and near infrared and UV).<br>
+**Rotationally symmetrical**,<br>
+**Thin**,<br>
+**2 polished surfaces** perpendicular to its axis of symmetry, **either or both curved** (and most often spherical).
+
+##### Classification of thin lenses
+
+**Convergent lenses** = **positive lenses** 
+
+![](lens-convergent-N3-en.jpeg)
+
+**Divergent lenses** = **negative lenses** 
+
+![](lens-divergent-N3-en.jpeg)
+
+### Brief chronology
+
+### Modeling a lens
+
+##### 
+
+