diff --git a/01.curriculum/01.physics-chemistry-biology/02.Niv2/04.optics/04.use-of-basic-optical-elements/01.plane-refracting-surface/02.plane-refracting-surface-overview/cheatsheet.en.md b/01.curriculum/01.physics-chemistry-biology/02.Niv2/04.optics/04.use-of-basic-optical-elements/01.plane-refracting-surface/02.plane-refracting-surface-overview/cheatsheet.en.md
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@@ -3,6 +3,64 @@ title: 'Spherical refracting surface  : overview'
 media_order: dioptre-1.gif
 ---
 
+### What is a refracting surface ? 
+
+#### Spherical refracting surface : physical description
+
+* Local **spherical interface separating two transparent media of different refractive indices**.
+
+* can be **foud in nature** : examples : when we look through the flat and quiet surface of a lake*, or when we look at something inside a fish ball aquarium.
+
+<!-- fig 1 to add-→
+<br>
+Fig. 1. The spherical refracting interface of a fish ball aquarium.
+
+* **appears in the design and modeling of other optical elements** : examples:<br>
+\- a glass window pane is the combinaison of two parallel plane refracting interfaces (air/glass, then glass/air) that are rotationaly symmetrical around a same axis.
+
+#### Spherical refracting interface versus 
+spherical refracting surface
+
+!!!! DIFFICULT  POINT:<br>
+!!!! A same plane or spherical plane refracting interface will have two different optical behaviors, will be modeled by two different sets of parameters, depending on the direction of the light propagation.
+!!!!
+!!!! Consider a plane interface (a thick window whose thickness and effect can be neglected) that separates air and water, and two twins (Thompson and Thomson) at equal distances on both sides of the interface.
+!!!!
+!!!! <!-- fig 2a to add --><br>
+!!!! Fig. 2a. The situation is not symmetrical :
+!!!!
+!!!! * When  Thompson (in air) looks at Thomson (in water) the light propagets from Thomson to Thompson's eyes. The fact is that Thompson sees the image of his brother closer than the real position of his brother.
+!!!!
+!!!! <!-- fig 2b to add--><br>
+!!!! Fig. 2b.
+!!!
+!!!! * In the opposite situation, when Thomson (in water) looks at his brother (in air), the light propagates from Thompson to Thomson's eyes. And the fact is that Thomson sees the image of his brother farther away from his real position.<br>
+!!!! (Strictly speaking, the eye of a fish should be considered in this situation, eyes well adapted to vision in water and in direct contact with water. If not, we should consider that the Thomson's dive mask is filled with water, to have Thomson's eyes in contact with water and not to add another water/air refracting surface (that of the dive mask) on the path of the light rays :
+!!!!
+!!!! <!-- fig 2c to add-→<br>
+!!!! Fig. 2c.
+!!!!
+!!!! All this can be predicted and calculated, but this example shows that this air/water plane refracting interface corresponds to two different plane refracting surfaces :
+!!!!
+!!!! * First case : refracting surface such as :<br>
+!!!! \- refractive index of the medium of incident light : $n_{inc}=n_{water}=1.33$<br>
+!!!! \- refractive index of the medium of emerging light : $n_{eme}=n_{air}=1$
+!!!!
+!!!! * Second case : for this refracting surface :<br>
+!!!! \- refractive index of the medium of incident light : $n_{inc}=n_{air}=1$<br>
+!!!! \- refractive index of the medium of emerging light : $n_{eme}=n_{water}=1.33$
+!!!!
+
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 ### Spherical refracting surface modeling.
 
 #### Description