Update textbook.fr.md

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

@@ -22,7 +22,7 @@ and a standing wave pattern along the y axis.
 _TE and TM waves and their corresponding standing wave behaviour along the y axis._
 
 
-For TE modes (TE = transverse-electric) we have:
+* For TE modes (TE = transverse-electric) we have:
 
 _equations_
 
@@ -66,7 +66,7 @@ height="1.7708333333333333in"}
 standing wave be- haviour along the *y* axis.
 ---------->
 
-and similarly for TM modes  (TM = transverse-magnetic)
+* Similarly for TM modes (TM = transverse-magnetic)
 
 _equations_
 
@@ -79,26 +79,18 @@ induction field (incident + reflected) to be zero:
 $`\overrightarrow{E}_{\parallel}=0\quad\text{and}\quad\overrightarrow{B}_{\perp}=0`$.   
 
   
-For TE modes this results in the fact that the total electric field
-$`\overrightarrow{E}`$~⊥~ (it is
->
-only tangential by definition) has nodes for *y* = *[nπ]{.underline}
-[nπ]{.underline}*
-
-*y*
-
-*[nλ]{.underline}*
->
-2 cos *θ*
->
-where
->
-*k~y~* = *k* cos *θ* is the *y* component of the wavevector. For TM
-modes, we have instead $`\overrightarrow{E}`$ *~,z~* = 0 as the *z* component of the
+* For TE modes,   
+this results in the fact that the total electric field
+$`\overrightarrow{E}_{\perp}`$  (it is only tangential by definition) has nodes for 
+$`y=\frac{}{}=\frac{}{}=\frac{}{}`$ where $`k_y=k\,\cos\theta`$ is the y component 
+of the wavevector.
+
+* For TM modes,   
+we have instead $`\overrightarrow{E}_{\parallel\,,z}=0`$ as the z component of the
 total electric field represents the tangential component.
->
-As the tangent component of the electric field is zero in the nodal
-planes
+
+As the tangent component of the electric field is zero in the nodal planes,   
+$`y=dfrac{\pi}{k_y}=dfrac{\pi}{k_y}=dfrac{\pi}{k_y}
 >
 *y* = *[π]{.underline} ,* [2*π*]{.underline} *,* [3*π*]{.underline}
 >