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 deleted file mode 100644 index 3a41df392..000000000 --- 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 +++ /dev/null @@ -1,182 +0,0 @@ ---- -title: 'new course : overview' -published: true -visible: true ---- - -### The mirror - -#### What is a mirror ? - -##### Objective - -* initial : to **reflect** light, to **focus or disperse light**. -* Ultimate : to **realize images**, alone or as part of optical instruments. - -##### Physical principle - -* uses the **phenomenon of reflection**, described by the law of reflection. - -##### Constitution - -* Usually plane or curved (spherical for the most simple to realize, -parabolic or elliptical) **surface, highly polished** so that its surface -state deviates from its theoretical form of less than $`\lambda/10`$ at each point -of its surface ($`\lambda`$ being the wavelength in vacuum of the light to be reflected). -To increase the reflectivity of the mirror (percentage of reflected light -intensity per the total of the incident light intensity), the surface is -**most often metallized**. - -##### 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. - -#### 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 whose radius of curvature tends towards infinity*. -Plane mirror, concave and convex spherical mirror - -![](plane-concave-convex-mirrors.png)
-Fig. 1. a) plane b) concave c) convex mirrors - -#### Are plane and spherical mirrors stigmatic? - -##### 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.
-$`\Longrightarrow`$ 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 mirrors with a limited aperture (see the angle $`\alpha`$ (rad) which is reduced 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 - -![](spherical-mirror-rays-stigmatism-1000-3.jpg)
-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. - - -##### Gauss conditions / paraxial approximation and quasi-stigmatism - -* 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 mirrors can be considered *quasi- stigmatic*, and therefore they -*can be used to build optical images*. - -* Mathematically, when an angle $`i`$ is small ($`i < or \approx 10 ^\circ`$), the following -approximations can be made :
-$`sin(i) \approx tan (i) \approx i`$ (rad), et $`cos(i) \approx 1`$. - -* Geometrical optics limited to Gaussian conditions is called **Gaussian optical** or **paraxial optics**. - -#### The thin spherical mirror (paraxial optics) - -* We call **thin spherical mirror** a *spherical mirror used in the Gauss conditions*. - -##### Analytical study (in paraxial optics) - -* **Spherical mirror equation** = **conjuction equation** for a spherical mirror :

-$`\dfrac{1}{\overline{SA_{ima}}}+\dfrac{1}{\overline{SA_{obj}}}=\dfrac{2}{\overline{SC}}`$  (equ.1) - -* **Transverse magnification expression** :

-$`\overline{M_T}=-\dfrac{\overline{SA_{ima}}}{\overline{SA_{obj}}}`$  (equ.2) - -You know $`\overline{SA_{obj}}`$ , calculate $`\overline{SA_{ima}}`$ using (equ. 1) -then $`\overline{M_T}`$ with (equ.2), and deduce $`\overline{A_{ima}B_{ima}}`$. - -! *USEFUL 1* :
-! 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 $`\overline{M_T}=+1`$. - -! *USEFUL 2* :
-! *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)
-! - to go from spherical to plane : $`|\overline{SC}|\longrightarrow\infty`$. -! Then we get for a plane mirror :
-! $`\overline{SA_{ima}}= - \overline{SA_{obj}}`$ and $`\overline{M_T}=+1`$ - -##### Graphical study - -*1 - Determining object and image focal points* - -Positions of object focal point F and image focal point F’ are easily obtained from the conjunction -equation (equ. 1). - -* Image focal length $`\overline{OF'}`$ : $`\left(|\overline{OA_{obj}}|\rightarrow\infty\Rightarrow A_{ima}=F'\right)`$

-(equ.1) $`\Longrightarrow\dfrac{1}{\overline{SF'}}=\dfrac{2}{\overline{SC}}\Longrightarrow\overline{SF'}=\dfrac{\overline{SC}}{2}`$ - -* Object focal length $`\overline{OF}`$ : $`\left(|\overline{OA_{ima}}|\rightarrow\infty\Rightarrow A_{obj}=F\right)`$

-(equ.2) $`\Longrightarrow\dfrac{1}{\overline{SF}}=\dfrac{2}{\overline{SC}}\Longrightarrow\overline{SF}=\dfrac{\overline{SC}}{2}`$ - -*2 - Thin spherical mirror representation* - -* **Optical axis = revolution axis** of the mirror, positively **oriented** in the direction of propagation of the incident light. - -* Thin spherical mirror equation :

-\-**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 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’**. - -##### Examples of graphical situations, with analytical results to train - - - -* with **real objects** - -![](Thin-spherical-mirror-InfAC-1000.jpg)
-Fig. 5. Concave mirror with object between infinity and C - -![](Thin-spherical-mirror-CAF-1000.jpg)
-Fig. 6. Concave mirror with object between C and F/F’ - -![](Thin-spherical-mirror-FAS-1000.jpg)
-Fig. 7. Concave mirror with object between F/F’ and S - -![](Thin-spherical-mirror-InfAS-1000.jpg)
-Fig. 8. Convex mirror - - - - - - - - - - - - - - - - - - - -