From 2a2fc7a18a9bb4caf2469f917db76aa26abab895 Mon Sep 17 00:00:00 2001 From: Claude Meny Date: Tue, 15 Oct 2019 18:22:31 +0200 Subject: [PATCH] Update cheatsheet.en.md --- .../02.new-course-overview/cheatsheet.en.md | 55 +++++++++---------- 1 file changed, 25 insertions(+), 30 deletions(-) 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 f1d554312..494508cad 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 @@ -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)
@@ -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.
A virtual object gives a real image. +* Object and image are symmetrical on both side of the surface of the plane mirror.
+$`\Longrightarrow`$ A real object gives a virtual image.
+        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)
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, +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 +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** :
-\- The *angles of incidence and refraction are small*
-(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** :
+\- The *angles of incidence are small*
+(the rays are slightly inclined on the optical axis, and intercept the spherical mirror in the vicinity of its vertex),
-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 :
-$`sin(\alpha) \approx tan (\alpha) \approx \alpha`$ (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* :
-! *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 :
-! $`n_{eme}=-n_{inc}`$
+! *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 :
+! - to go from refracting surface to mirror : $`n_{eme}=-n_{inc}`$
! (to memorize : medium of incidence=medium of emergence, therefor same speed of light, but direction ! of propagation reverses after reflection on the mirror)
-! 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 :
-! $`\overline{SA_{ima}}=\overline{SA_{obj}}`$ 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.

-\-**vertex S**, that locates the refracting surface on the optical axis;

+\-**vertex S**, that indicates the position of the mirror along the optical axis;

\-**nodal point C = center of curvature**.

\-**object focal point F** and **image focal point F’**.