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

@@ -56,7 +56,37 @@ Fig. 1. a) plane    b) concave    c) convex   mirrors
 * 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.)
+* 
+![](spherical-mirror-rays-stigmatism-1000-1.jpg)
+Fig. 2. Non stigmatism of a convexe mirror.
 
+![](spherical-mirror-rays-stigmatism-1000-2.jpg)
+Fig. 3. But when we limit the aperture of the mirror,
+
+![](spherical-mirror-rays-stigmatism-1000-3.jpg)
+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
+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 
+vicinity of its vertex),<br>
+then the spherical refracting surfaces 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 
+approximations can be made :<br>
+$`sin(\alpha) \approx  tan (\alpha) \approx \alpha`$ (rad), et $`cos(\alpha) \approx 1`$.
+
+* Geometrical optics limited to Gaussian conditions is called **Gaussian optical** or **paraxial optics**.
+ 
+#### The thin spherical mirror (paraxial optics)