Update textbook.fr.md

12.temporary_ins/96.electromagnetism-in-media/20.reflexion-refraction-at-interfaces/20.metallic-waveguides/10.main/textbook.fr.md

@@ -212,53 +212,21 @@ and
 
 $`v_{\varphi}=\dfrac{\omega}{k_z}=\dfrac{c}{\sqrt{1-\frac{\omega_c^2}{\omega^2}}}`$
 
+It is a dispersive medium.
 
+![](dispersion-relation-for-a-mode_temp_L1200.jpg)   
+_Fig. 4.4: The geometric interpretation of the dispersion._
 
-
-
-*π*2*n*2 (4.5)
->
-*b*
->
-*v* = = = *f* (*ω*) (4.6)
-
-*ϕ kz*
-
-j1 −
->
-*[ω]{.underline}c*[2]{.underline} *ω*2
->
-![](media/image219.png)
-
-Figure 4.4: A dispersion relation for a mode.
-
-it is a dispersive medium.
->
 Similarly we obtain for the group velocity:
 
-*v~g~*
-
-chap5 Geometrical interpretation
-
-= *[∂ω]{.underline}*
->
-*∂k~z~*
-
-2
-
-= *c* 1 − *c*
->
-(4.7)
-
-![](media/image228.png)
+$`v_{\varphi}=\drac{\partial \omega}{\partial k_z}=c\,\sqrt{1-\dfrac{\omega_c^2}{\omega^2}}`$
 
-![](media/image230.png)
-![](media/image231.png){width="2.0771489501312335in"
-height="1.171874453193351in"}
+__Geometrical interpretation__
 
-Figure 4.5: The geometric interpretation of the dispersion.
+![](geometrical-interpretation-of-the-dispersion_temp_L1200.jpg)   
+_Fig. 4.5: The geometric interpretation of the dispersion._
 
-We can understand the propagating behaviour of the TE wave using a
+We can understand the propagating behaviour of the $`TE`$ wave using a
 simple interpretation:
 
 -   For *ω* = *ω~c~*, *k~z~* = *k* sin *θ* =0. This implies *θ* = 0. The