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

@@ -169,11 +169,25 @@ You know $`\overline{SA_{obj}}`$, $`n_{inc}`$ and $`n_{eme}`$, you have previous
 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>
-&nbsp;&nbsp;&nbsp;&nbsp;(equ.1)$`\Longrightarrow\dfrac{n_{eme}}{\overline{SF'}}=\dfrac{n_{eme}-n_{inc}}{\overline{SC}}`$$`\Longrightarrow\overline{SF'}=\dfrac{n_{eme}\cdot\overline{SC}}{n_{eme}-n_{inc}}`$
+&nbsp;&nbsp;&nbsp;&nbsp;(equ.1)$`\Longrightarrow\dfrac{n_{eme}}{\overline{SF'}}=\dfrac{n_{eme}-n_{inc}}{\overline{SC}}`$
+$`\Longrightarrow\overline{SF'}=\dfrac{n_{eme}\cdot\overline{SC}}{n_{eme}-n_{inc}}`$ &nbsp;&nbsp;(equ.4)
 
 * Object focal length $`\overline{OF}`$ : $`\left(|\overline{OA_{ima}}|\rightarrow\infty\Rightarrow A_{obj}=F\right)`$<br>
-&nbsp;&nbsp;&nbsp;&nbsp;(equ.1) $`\Longrightarrow-\dfrac{n_{inc}}{\overline{SF}}=\dfrac{n_{eme}-n_{inc}}{\overline{SC}}`$$`\Longrightarrow\overline{SF}=-\dfrac{n_{inc}\cdot\overline{SC}}{n_{eme}-n_{inc}}
-`$
+&nbsp;&nbsp;&nbsp;&nbsp;(equ.1) $`\Longrightarrow-\dfrac{n_{inc}}{\overline{SF}}=\dfrac{n_{eme}-n_{inc}}{\overline{SC}}`$
+$`\Longrightarrow\overline{SF}=-\dfrac{n_{inc}\cdot\overline{SC}}{n_{eme}-n_{inc}}`$ &nbsp;&nbsp;(equ.5)
+
+!!!! *ADVISE* :<br>
+!!!! Memory does not replace understanding. Do not memorise (equ.4) and (equ.5)), but understand
+!!!! the definitions of the object and image focal points, and know how to find these two equations 
+!!! from the conjuction equation for a spherical refracting surface.
+!!!!
+
+! *NOTE* :<br>
+! An optical element being convergent if the image focal point is real, 
+! so if $`\overline{OF}>0`$ (with optically axis positively oriented in the direction of the light propagation), 
+! you can deduce from (equ.4)) that is spherical refracting surface is convergent if and only if its center
+! of curvature C is in the mmedium of highest refractive index.
+!
 
 ##### 2 - Thin spherical refracting surface representation