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 index c6c08cdc2..b5cf02432 100644 --- 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 @@ -62,7 +62,7 @@ refracting interface corresponds to two different plane refracting surfaces :
!!!! 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* :
-!!!! 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*.
-!!!! _A crystal ball forms a spherical refracting surface : un "dioptre sphérique" in French._ -!!!! -!!!! unit of measure : *EN : dioptre* , *ES : dioptría* , *FR : dioptrie*.
-!!!! _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

+**$`\dfrac{n_{eme}}{\overline{SA_{ima}}}-\dfrac{n_{inc}}{\overline{SA_{obj}}}=\dfrac{n_{eme}-n_{inc}}{\overline{SC}}`$**   (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**

+ **$`\overline{M_T}=\dfrac{n_{inc}\cdot\overline{SA_{ima}}}{n_{eme}\cdot\overline{SA_{obj}}}`$**   (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 $`|\overline{SC}|\longrightarrow\infty`$.
Then we get *for a plane refracting surface :* ! -! * *conjuction equation :*   $`\dfrac{n_{fin}}{\overline{SA_{ima}}}-\dfrac{n_{ini}}{\overline{SA_{obj}}}=0`$. -! -! * *transverse magnification equation :*   $`\dfrac{n_{ini}\cdot\overline{SA_{ima}}}{n_{fin}\cdot\overline{SA_{obj}}}`$    (unchanged). +! * *conjuction equation :*   $`\dfrac{n_{fin}}{\overline{SA_{ima}}}-\dfrac{n_{ini}}{\overline{SA_{obj}}}=0`$    (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 :*   $`\dfrac{n_{ini}\cdot\overline{SA_{ima}}}{n_{fin}\cdot\overline{SA_{obj}}}`$ +   (equ.2, unchanged)

+but (equ.3) gives $`\dfrac{\overline{SA_{ima}}}{\overline{SA_{obj}}}=\dfrac{n_{inc}}{n_{eme}}`$.
+Copy this result into (equ.2) leads to $`\overline{M_T}=+1`$. #### Graphical study \ No newline at end of file