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-title : lens-overview
-published: false
-visible: false
-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'
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-TO REWRITE COMPLETELY
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-### 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.
-
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-
-_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
-
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-!!! 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**
-
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-
-**Divergent lenses** = **negative lenses**
-
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-
-### Brief chronology
-
-### Modeling a lens
-
-#####
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