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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* :
+!!! 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.
+! * 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)*
+* (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 :
+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 :
+
+
+
+##### 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.
+
+
+
+
+_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
+
+
+
+
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+
+
+### The thin lens
+
+##### Objective
+to **focuse or disperse the light**,
+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 $`\delta`$
+ 1 diopter = 1 $`\delta`$ = 1 $`m^{-1}`$).
+* **positive vergence** ($`V>0)\:\Longleftrightarrow`$ *light focalisation : convergent lens*.
+* **negative vergence** ($`V<0)\:\Longleftrightarrow`$ *light dispersion : divergent lens*.
+* **absolute value** of the vergence ($`|V|`$) : *increases as the optical phenomenon (focalisation or dispersion) increases*
+* (as the corresponding deviation of light rays increases).
+* **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*
+* **negative $`f'`$** ($`f'<0)\:\Longleftrightarrow`$ *disperse light : divergent lens*
+* **absolute value of $`f'`$** ($`|f'|`$) : *decreases as the optical phenomenon (focalisation or dispersion) increases*.
+* **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 :
+! $`\Longrightarrow`$ object focal lenght $`f`$ is the opposite of image focal length $`f'`$ : $`f=-f'`$
+! $`\Longrightarrow`$ 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).
+**Rotationally symmetrical**,
+**Thin**,
+**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**
+
+
+
+**Divergent lenses** = **negative lenses**
+
+
+
+### Brief chronology
+
+### Modeling a lens
+
+#####
+
+