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-title: 'new course : overview'
-published: true
-visible: true
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-
-### 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
-
-
-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.
-
-
-Fig. 2. Non stigmatism of a convexe mirror.
-
-
-Fig. 3. But when we limit the aperture of the mirror
-
-
-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**
-
-
-Fig. 5. Concave mirror with object between infinity and C
-
-
-Fig. 6. Concave mirror with object between C and F/F’
-
-
-Fig. 7. Concave mirror with object between F/F’ and S
-
-
-Fig. 8. Convex mirror
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