suite

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

@@ -62,7 +62,7 @@ refracting interface corresponds to two different plane refracting surfaces :<br
 !!!! \- refracting index of the medium of the emergent light : $n_{eme} = n_{water} = 1.33$.
 !!!!
 
-#### 
+#### Difference in terminology between Spanish, French and English
 
 !!!! *BE CAREFUL* :<br>
 !!!! In the same way as we use in English the single word "mirror" to qualify a "reflecting surface", in French is use the single word "dioptre" to qualify a "refracting surface".
@@ -119,7 +119,7 @@ $`sin(\alpha) \approx  tan (\alpha) \approx \alpha`$, and $`cos(\alpha) \approx
 We call **thin spherical refracting surface** a spherical refracting surface *used in the Gauss conditions*.
 
 
-### How is modeled  in paraxial optics ?
+### How is modeled a spherical refracting surface in paraxial optics ?
 
 
 #### Characterization of a spherical refracting surface
@@ -132,72 +132,30 @@ which defines $`\overline{SC}`$ : algebraic distance between vertex S and center
 \- **$`n-{eme} : refractive index of the medium of the emergent light**.
 
 * 1 arrow : indicates the *direction of light propagation*
-
-#### Analytical study 
-
-
-
-
-### Spherical refracting surface modeling.
-
-#### Description 
-
+* 
 ![](dioptre-1.gif)
 
-with :
-* arrow : indicates direction of light propagation.
-* $`n_{ini}`$ : refractive index of the initial medium.
-* $`n_{fin}`$ : refractive index of the final medium.
-* $`\overline{SC}`$ : algebraic distance between vertex S and center C of curvature on optical axis.
-
-
-
-!!!! *BE CAREFUL* :<br>
-!!!! In the same way as we use in English the single word "mirror" to qualify a "reflecting surface", in French is use the single word "dioptre" to qualify a "refracting surface".
-!!!! The term "dioptre" in English is a unit of mesure of the vergence of an optical system. In French, the same unit of measure is named "dioptrie".
-!!!! So keep in mind the following scheme :
-!!!!
-!!!! refracting surface : *EN : refracting surface* , *ES : superficie refractiva* , *FR : dioptre*.<br>
-!!!! _A crystal ball forms a spherical refracting surface : un "dioptre sphérique" in French._
-!!!!
-!!!! unit of measure : *EN : dioptre* , *ES : dioptría* , *FR : dioptrie*.<br>
-!!!! _My corrective lens for both eyes are 4 dioptres : "4 dioptries" in French._
-
-
-#### Spherical refracting surface.
 
-#### Analytical study
-
-A **spherical refracting surface** in analytical paraxial optics is defined by *three quantities* :
-* **$`n_{ini}`$** : *refractive index of the initial medium* (the medium on the side on the incident light).
-* **$`n_{fin}`$** : *refractive index of the final medium* (the medium on the side on the emerging light, after crossing the refracting surface).
-* **$`\overline{SC}`$** : the *algebraic distance between the __vertex S__* (sometimes called "pole", is the centre of the aperture) *and the __center of curvature C__* of the refracting surface.
-
-! *USEFUL* : The whole analytic study below also applies to a plane refracting surface. We just need to remark that a plane surface is a spherical surface whose radius of curvature tends towards infinity.
-
-##### Spherical refracting surface equation
-
-**spherical refracting surface equation** = **"conjuction equation" for a spherical refracting surface**
-
-**$`\dfrac{n_{fin}}{\overline{SA_{ima}}}-\dfrac{n_{ini}}{\overline{SA_{obj}}}=\dfrac{n_{fin}-n_{ini}}{\overline{SC}}`$**
+#### Analytical study 
 
-##### Transverse magnification expression
 
-2. I use the **"transverse magnification equation" for a spherical refracting surface**, to calculate the *__algebraic value__ of the transverse magnification* **$`\overline{M_T}`$**, then to derive the *__algebraic length__* **$`\overline{A_{ima}B_{ima}}`$** of the segment $`[A_{ima}B_{ima}]`$, that is the algebraic distance of the point image $`B_{ima}`$ from its orthogonal projection $`A_{ima}`$ on the optical axis.
+* **Thin spherical refracting surface equation** = **conjuction equation** for a spherical refracting surface<br><br>
+**$`\dfrac{n_{eme}}{\overline{SA_{ima}}}-\dfrac{n_{inc}}{\overline{SA_{obj}}}=\dfrac{n_{eme}-n_{inc}}{\overline{SC}}`$**&nbsp;&nbsp;  (equ.1)
 
-By *definition :* **$`\overline{M_T}=\dfrac{\overline{A_{ima}B_{ima}}}{\overline{A_{obj}B_{obj}}}`$**.
-Its *expression for spherical refracting surface :* **$`\overline{M_T}=\dfrac{n_{ini}\cdot\overline{SA_{ima}}}{n_{fin}\cdot\overline{SA_{obj}}}`$**.
+* **Transverse magnification expression**<br><br>
+ **$`\overline{M_T}=\dfrac{n_{inc}\cdot\overline{SA_{ima}}}{n_{eme}\cdot\overline{SA_{obj}}}`$**&nbsp;&nbsp;  (equ.2)
 
-I know $`\overline{SA_{obj}}$, $n_{ini}$ and $n_{fin}$, I have previously calculated $`\overline{SA_{ima}}$, so I can calculate $`\overline{M_T}`$ and deduced $`\overline{A_{ima}B_{ima}}`$
+You know $`\overline{SA_{obj}}$, $n_{inc}$ and $n_{eme}`$, you have previously calculated $`\overline{SA_{ima}}`$, so you can calculate $`\overline{M_T}`$ and deduced $`\overline{A_{ima}B_{ima}}`$.
 
 
 ! *USEFUL* : The conjuction equation and the transverse magnification equation for a plane refracting surface are obtained by rewriting these equations for a spherical refracting surface in the limit when $`|\overline{SC}|\longrightarrow\infty`$.<br> Then we get *for a plane refracting surface :*
 !
-! * *conjuction equation :*&nbsp;&nbsp; $`\dfrac{n_{fin}}{\overline{SA_{ima}}}-\dfrac{n_{ini}}{\overline{SA_{obj}}}=0`$.
-!
-! * *transverse magnification equation :*&nbsp;&nbsp; $`\dfrac{n_{ini}\cdot\overline{SA_{ima}}}{n_{fin}\cdot\overline{SA_{obj}}}`$ &nbsp;&nbsp; (unchanged).
+! * *conjuction equation :*&nbsp;&nbsp; $`\dfrac{n_{fin}}{\overline{SA_{ima}}}-\dfrac{n_{ini}}{\overline{SA_{obj}}}=0`$ &nbsp;&nbsp; (equ.3)
 !
-! This generalizes and completes the knowledge you get about plane refracting surfaces seen in your pedagogical paths in plain and hills.
+! * *transverse magnification equation :*&nbsp;&nbsp; $`\dfrac{n_{ini}\cdot\overline{SA_{ima}}}{n_{fin}\cdot\overline{SA_{obj}}}`$
+&nbsp;&nbsp; (equ.2, unchanged)<br><br>
+but (equ.3) gives $`\dfrac{\overline{SA_{ima}}}{\overline{SA_{obj}}}=\dfrac{n_{inc}}{n_{eme}}`$.<br>
+Copy this result into (equ.2) leads to $`\overline{M_T}=+1`$.
 
 
 #### Graphical study