diff --git a/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 b/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 index aa4dc948e..4d340162c 100644 --- a/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 +++ b/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** :
+\- The *angles of incidence and refraction are small*
+(the rays are slightly inclined on the optical axis, and intercept the spherical surface in the +vicinity of its vertex),
+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 :
+$`sin(\alpha) \approx tan (\alpha) \approx \alpha`$ (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)