Update cheatsheet.en.md

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

@@ -88,6 +88,37 @@ $`sin(\alpha) \approx  tan (\alpha) \approx \alpha`$ (rad), et $`cos(\alpha) \ap
  
 #### The thin spherical mirror (paraxial optics)
 
+* We call **thin spherical mirror** a *spherical mirror used in the Gauss conditions*.
+
+##### Analytical study (in paraxial optics)
+
+* **Spherical mirror equation** = **conjuction equation** for a spherical mirror :<br><br>
+$`\dfrac{1}{\overline{SA_{ima}}}+\dfrac{1}{\overline{SA_{obj}}}=\dfrac{2}{\overline{SC}}`$&nbsp;&nbsp;(equ.1)
+
+* **Transverse magnification expression** :<br><br>
+$`\overline{M_T}=-\dfrac{\overline{SA_{ima}}}{\overline{SA_{obj}}}`$$&nbsp;&nbsp;(equ.2)
+
+You know $`\overline{SA_{obj}}`$ , calculate $`\overline{SA_{ima}}`$ using (equ. 1) 
+then $`\overline{M_T}`$ with (equ.2), and deduce $`\overline{A_{ima}B_{ima}}`$.
+
+! *USEFUL 1° :<br>
+! 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
+! $`\overline{M_T}=+1`$.
+
+! *USEFUL 2° :<br>
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