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

@@ -27,16 +27,15 @@ intensity per the total of the incident light intensity), the surface is
 
 ##### Interest in optics
 
-* **One of the most importante simple optical component** that is used *alone or 
-* combined in a series in most optical instruments* : some telephotos, 
-* reflecting telescopes.
+* **One of the most importante simple optical component** that is used *alone or combined in a series in most optical instruments* :
+some telephotos, reflecting telescopes.
 
 #### Why to study plane and spherical mirrors?
 
 * **Plane and spherical mirrors** are the *most technically easy to realize*, 
 so they are the *most common and cheap*.
 * In paraxial optics, the optical properties of a **plane mirror** are those 
-of a *spherical mirror of infinite radius of curvature*.
+of a *spherical mirror whose radius of curvature tends towards infinity*.
 Plane mirror, concave and convex spherical mirror
 
 ![](plane-concave-convex-mirrors.png)<br>
@@ -47,42 +46,40 @@ Fig. 1. a) plane    b) concave    c) convex   mirrors
 ##### Perfect stigmatism of the plane mirror
 
 * A plane mirror is **perfectly stigmatic**.
-* Object and image are symmetrical on both side of the surface of the plane mirror.
-* A real object gives a virtual image.<br> A virtual object gives a real image.
+* Object and image are symmetrical on both side of the surface of the plane mirror.<br>
+$`\Longrightarrow`$ A real object gives a virtual image.<br> 
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; nbsp;&nbsp;A virtual object gives a real image.
 
 ##### Non stigmatism of the spherical mirror
 
 * In each point of the spherical mirror, the law of reflection applies.
-* A spherical mirror is not stigmatic: The rays (or their extensions) 
-* coming from an object point generally do not converge towards an image 
-* point (see Fig. 2.)
-* 
+* A spherical mirror is not stigmatic: The rays (or their extensions) coming from an object point generally do not converge towards an image point (see Fig. 2.)
+* A spherical mirrors with a limited aperture (see the angle $`\alpha`$ (rad) lower on Fig. 3. and 4.) and used so that 
+angles of incidence remain small (see Fig. 4.) become quasi-stigmatic.
+
 ![](spherical-mirror-rays-stigmatism-1000-1.jpg)<br>
 Fig. 2. Non stigmatism of a convexe mirror.
 
 ![](spherical-mirror-rays-stigmatism-1000-2.jpg)<br>
-Fig. 3. But when we limit the aperture of the mirror,
+Fig. 3. But when we limit the aperture of the mirror
 
 ![](spherical-mirror-rays-stigmatism-1000-3.jpg)<br>
-Fig. 4 . and limit the conditions of use to small angles of incidence and 
-refraction are small, then a point image can be defined : the mirror becomes
+Fig. 4 . and limit the conditions of use to small angles of incidence, then a image point can almost be defined : the mirror becomes
 quasi-stigmatic.
 
-* Spherical mirrors with a limited aperture (see Fig. 3.) and used so that 
-angles of incense and emergence remain small (see Fig. 4.), become quasi-stigmatic.
 
 ##### Gauss conditions / paraxial approximation and quasi-stigmatism
 
-* When spherical refracting surfaces are used under the following conditions, named **Gauss conditions** :<br>
-\- The *angles of incidence and refraction are small*<br>
-(the rays are slightly inclined on the optical axis, and intercept the spherical surface in the 
+* When spherical mirrors are used under the following conditions, named **Gauss conditions** :<br>
+\- The *angles of incidence are small*<br>
+(the rays are slightly inclined on the optical axis, and intercept the spherical mirror in the 
 vicinity of its vertex),<br>
-then the spherical refracting surfaces can be considered *quasi- stigmatic*, and therefore they 
+then the spherical mirrors can be considered *quasi- stigmatic*, and therefore they 
 *can be used to build optical images*.
 
-* Mathematically, when an angle $`\alpha`$ is small ($`\alpha < or \approx 10 ^\circ`$), the following 
+* Mathematically, when an angle $`i`$ is small ($`i < or \approx 10 ^\circ`$), the following 
 approximations can be made :<br>
-$`sin(\alpha) \approx  tan (\alpha) \approx \alpha`$ (rad), et $`cos(\alpha) \approx 1`$.
+$`sin(i) \approx  tan (i) \approx i`$ (rad), et $`cos(i) \approx 1`$.
 
 * Geometrical optics limited to Gaussian conditions is called **Gaussian optical** or **paraxial optics**.
  
@@ -105,19 +102,17 @@ 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
-! $`\overline{M_T}=+1`$.
+! 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>
-! $`n_{eme}=-n_{inc}`$<br>
+! *You can find* the conjunction and the transverse magnification *equations for a plane or spherical mirror as well as for a plane refracting surface directly from 
+! those of the spherical refracting surface*, with the following assumptions :<br>
+! - to go from refracting surface to mirror : $`n_{eme}=-n_{inc}`$<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>
-! are obtained by rewriting these two equations for a spherical refracting surface in the limit 
-! when $`|\overline{SC}|\longrightarrow\infty`$.
+! - to go from spherical to plane : $`|\overline{SC}|\longrightarrow\infty`$.
 ! Then we get for a plane mirror :<br>
-! $`\overline{SA_{ima}}=\overline{SA_{obj}}`$ and $`\overline{M_T}=+1`$
+! $`\overline{SA_{ima}}= - \overline{SA_{obj}}`$ and $`\overline{M_T}=+1`$
 
 ##### Graphical study
 
@@ -140,7 +135,7 @@ equation (equ. 1).
 \-**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>
+\-**vertex S**, that indicates the position of the mirror along the optical axis;<br><br>
 \-**nodal point C = center of curvature**.<br><br>
 \-**object focal point F** and **image focal point F’**.