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title: 'new course : main'
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!!!! *LESSON  UNDER  CONSTRUCTION :* <br>
!!!! Non published but invisible
!!!! This course is *under construction*, it is *not approved by the pedagogical team* at this stage. <br>
!!!! Working document intended only for the pedagogical team.

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### A lens

An optical **lens** is a very common and *simple optical element*, *designed and made to focuse or disperse the light* by the use of the refraction phenomenon. Because requires to focus in a point image the light emitted or diffused by any object point

<!--Optical lenses are the most important tools in optical design for controlling light. When optical designers talk about optical lenses, they are either referring to a single lens element or an assembly of lens elements (Figure 1). -->

A lens is a **piece of transparent glass, quartz or plastic** that usually exhibits a *symmetry of revolution* about an axis<!-- or  being rotationally symmetrical-->. Its thickness, along its axis of symmetry, is small compared to the radius of its* two main surfaces* that are *polished and either or both curved*.

The **curvation of each surface** can be charactérized as :
* *convex* : the surface bulges outwards in the center.
* *concave* : the surface curves inward in the center.
* *plane* : the surface is plane.

In the ideal case of lenses with negligeable thicknesses (_thin lenses_) or optical systems with negligeable length (_thin lenses, mirrors and refracting surfaces in contact_) :
* The dioptric power (or vergence) $\delta$ of a *thin* lens is simply the sum of the dioptric powers  $\delta_{DS1}$ and $\delta_{DS2}$ of the two refracting surfaces $DS1$ and $DS2$ <!--interfaces? --> that compose the thin lens : $\delta=\delta_{DS1}+\delta_{DS2}$.
* The dioptric power (vergence) $\delta$ of *thin lenses in contact or in contact with a mirror* is simply the sum of their individual dioptric powers $\delta_i$ : $\delta=\sum \delta_i$.

In the more realistic and physical case, add a simple optical element of positive (respectively negative) dioptric power (or vergence) to an optical system will increase (resp. decrease) the total dioptric power of the system, so will increase the focalisation (resp. dispersion) of an incident light beam by the system.


!! *Beyond* :
!!
!! Lentils gave lenses their name



The final objective of lenses is to realize images, in the plane of a sensor to be recordered or to be seen with the naked eye. For this a 
