From f0b55e147a080a4dfef3817942aaaabc37ac76a3 Mon Sep 17 00:00:00 2001
From: Claude Meny <claude.meny@irap.omp.eu>
Date: Wed, 9 Oct 2019 23:32:33 +0200
Subject: [PATCH] Update cheatsheet.en.md

---
 .../02.new-course-overview/cheatsheet.en.md   | 44 ++++++++++++++++---
 1 file changed, 39 insertions(+), 5 deletions(-)

diff --git a/01.curriculum/01.physics-chemistry-biology/02.Niv2/04.optics/04.use-of-basic-optical-elements/02.mirror/02.new-course-overview/cheatsheet.en.md b/01.curriculum/01.physics-chemistry-biology/02.Niv2/04.optics/04.use-of-basic-optical-elements/02.mirror/02.new-course-overview/cheatsheet.en.md
index f20356b4f..b7b26f258 100644
--- a/01.curriculum/01.physics-chemistry-biology/02.Niv2/04.optics/04.use-of-basic-optical-elements/02.mirror/02.new-course-overview/cheatsheet.en.md
+++ b/01.curriculum/01.physics-chemistry-biology/02.Niv2/04.optics/04.use-of-basic-optical-elements/02.mirror/02.new-course-overview/cheatsheet.en.md
@@ -105,21 +105,55 @@ then $`\overline{M_T}`$ with (equ.2), and deduce $`\overline{A_{ima}B_{ima}}`$.
 ! The conjunction equation and the transverse magnification equation for a plane mirror 
 ! are obtained by rewriting these two equations for a spherical mirror in the limit when
 ! $`|\overline{SC}|\longrightarrow\infty`$.
-! Then we get for a plane mirror :$`\overline{SA_{ima}}=\overline{SA_{obj}}`$ and
+! Then we get for a plane mirror : $`\overline{SA_{ima}}=\overline{SA_{obj}}`$ and
 ! $`\overline{M_T}=+1`$.
 
 ! *USEFUL 2° :<br>
 ! *You can find* the conjunction and the transverse magnification **equations for a plane mirror directly from 
-! those of the spherical mirror**, with the following assumptions :<br><br>
-! $`n_{eme}=-n_{inc}`$<br><br>
+! those of the spherical mirror**, with the following assumptions :<br>
+! $`n_{eme}=-n_{inc}`$<br>
 ! (to memorize : medium of incidence=medium of emergence, therefor same speed of light, but direction
-! of propagation reverses after reflection on the mirror)<br><br>
-!
+! of propagation reverses after reflection on the mirror)<br>
 ! are obtained by rewriting these two equations for a spherical refracting surface in the limit 
 ! when $`|\overline{SC}|\longrightarrow\infty`$.
 ! Then we get for a plane mirror :<br>
 ! $`\overline{SA_{ima}}=\overline{SA_{obj}}`$ and $`\overline{M_T}=+1`$
 
+##### Graphical study
+
+*1 - Determining object and image focal points*
+
+Positions of object focal point F and image focal point F’ are easily obtained from the conjunction
+equation (equ. 1).
+
+* Image focal length $`\overline{OF'}`$ : $`\left(|\overline{OA_{obj}}|\rightarrow\infty\Rightarrow A_{ima}=F'\right)`$<br><br>
+(equ.1) $`\Longrightarrow\dfrac{1}{\overline{SF'}}=\dfrac{2}{\overline{SC}}\Longrightarrow\overline{SF'}=\dfrac{\overline{SC}}{2}`$
+
+* Object focal length $`\overline{OF}`$ : $`\left(|\overline{OA_{ima}}|\rightarrow\infty\Rightarrow A_{obj}=F\right)`$<br><br>
+(equ.2) $`\Longrightarrow\dfrac{1}{\overline{SF}}=\dfrac{2}{\overline{SC}}\Longrightarrow\overline{SF}=\dfrac{\overline{SC}}{2}`$
+
+*2 - Thin spherical mirror representation*
+
+* **Optical axis = revolution axis** of the mirror, positively **oriented** in the direction of propagation of the incident light.
+
+* Thin spherical mirror equation :<br><br>
+\-**line segment**, perpendicular to the optical axis, centered on the axis with symbolic *indication of the 
+direction of curvature* of the surface at its extremities, and *dark or hatched area on the non-reflective 
+side* of the mirror.<br><br>
+\-**vertex S**, that locates the refracting surface on the optical axis;<br><br>
+\-**nodal point C = center of curvature**.<br><br>
+\-**object focal point F** and **image focal point F’**.
+
+##### Examples of graphical situations, with analytical results to train
+
+* with **real objects** 
+
+
+
+
+
+
+