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title : lens-overview |
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media_order: 'lens-convergent-N3-en.jpeg,lens-divergent-N3-en.jpeg,Const_lens_conv_point_AavantF2.gif,thick-lens-water-air.gif,Lentille_epaisse_Gauss_incl_v1.gif,2-centered-refracting-surfaces-1-all.gif,2-refracting-surface-physical-system.jpeg,2-centered-refracting-surfaces-direction-axis.gif,Lentille_epaisse_principe_ok.gif,lentille_relle_representation_v1.gif,Const_lens_conv_point_AapresO.gif,lens-convergent-N3-es.jpeg,lens-convergent-N3-fr.jpeg,lens-divergent-N3-es.jpeg,lens-divergent-N3-fr.jpeg' |
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### Two successive and centered spherical refracting surfaces |
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!!! *WHERE YOU ARE* :<br> |
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!!! Observation $`\Rightarrow`$ Geometrical optic interpretation $`\Rightarrow`$ Fermat's Principle $`\Rightarrow`$ |
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The 5 optical laws $`\Rightarrow`$ Paraxial approximation $`\Rightarrow`$ Simple optical element $`\Rightarrow`$ System |
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of 2 simple optical elements. |
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! *THIS CHAPTER AIMS AT* : |
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! * Deeply understand and better master thin lenses.<br> |
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! * Understand when the lens equation and the coresponding transverse magnification expression can be used, and when they are not correct. |
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! * Understand need and requirement of new concepts to master esaily and efficientlynext main chapter "Centered optical systems". |
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*Two successive and centered spherical refracting surfaces* = **thick lens** |
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##### Thick lens as a physical system |
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**Physical system** = *spatial distribution of the refracting indexes values* (_variations of refracting index can |
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be discontinuous with interfaces (_refracting surfaces, lenses, mirrors_) or continuous (graded-index optical fiber)_. |
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**Optical system** = *oriented physical system* = *physical systems + bodies (1) + a direction (2)* <br> |
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* (1) : which emit, diffuse or reflect the ambiant light. |
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* (2) : direction of light propagation considered through the physical system. |
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**Difference** between physical and optical system in optics : |
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Example of the lensball : |
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Physical system of a lensball : |
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**Thick lens** physical system :<br> |
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Most general : *3 different transparent media with their own refractive index values*, and *2 local spherical interfaces* |
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that separate these media, and *centered on the straigth line* that joins their centers of curvature._ |
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**Examples** in images : |
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##### Thick lens as an optical system |
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**Optical system** = *oriented physical system* = *physical systems + bodies (1) + a direction (2)* |
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* (1) : which emit, diffuse or reflec the ambiant light |
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* (2) : direction of light propagation considered through the two refracting surfaces. |
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*From physical system to optical system* : **a scenario to build** : |
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* Where is the object that is imaged ? |
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* In what direction are we searching for images ? |
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* what are the reflecting or refracting interfaces we take into account. |
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<!--To define an optical system, you have to find a scenario : where is the objet to be imaged or viewed ? |
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And where is the real image of the object to be registered by a matrix sensor or where is located the eye of |
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the observator ? This gives you the direction of propagation (from object to real image or eye) through the optical |
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system. This direction of propagation is part of the description of the optical system. In the figure above the optical |
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systems are each time two ordered spherical refracting surfaces._--> |
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_The physical system consists of two bubble aquariums side by side. In each of them, a fish, and the two fish, Jones and |
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Tessa face each other. These two situations correspond to two optical systems: "Tessa looks at Jones" and "Jones looks at Tessa" |
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(the order of crossing of the refracting surfaces by the light is reversed in both cases). In the situtation we want to describe, |
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the direction of the light is indicated (the brown arrow in the figures)_ |
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**Graphical representation** (drawing) and **analytical representation** (*3 algebraic distances* : 2 radius of curvature |
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$`\overline{S_1C_1}`$, $`\overline{S_2C_2}`$,+ distance between the two vertices of the refracting surfaces $`\overline{S_1S_2}`$ |
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*when used in the paraxial (or same, gaussian) approximation, so when considered in paraxial optics. |
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_ In order to identify conjugated points, to construct the final image of a specific object for example, the optical axis |
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of the optical system is plotted, vertices and centers of curvature of spherical refracting surfaces are localised on the optica |
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l axis. Because |
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!!! Thick lens |
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### The thin lens |
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##### Objective |
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to **focuse or disperse the light**,<br> |
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with often the final goal, alone or as part of optical instruments, to **realize images**. |
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##### Physical principle |
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**uses the refractive phenomenon**, described by the Snell-Descartes' law. |
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##### Characterization of its efficiency |
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(efficiency to realize its objective) |
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**Vergence** = **dioptric power** V of the lens : |
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* **unit** : in S.I. : the *diopter*, of symbol $`\delta`$<br> |
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1 diopter = 1 $`\delta`$ = 1 $`m^{-1}`$). |
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* **positive vergence** ($`V>0)\:\Longleftrightarrow`$ *light focalisation : convergent lens*.<br> |
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* **negative vergence** ($`V<0)\:\Longleftrightarrow`$ *light dispersion : divergent lens*.<br> |
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* **absolute value** of the vergence ($`|V|`$) : *increases as the optical phenomenon (focalisation or dispersion) increases* |
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* (as the corresponding deviation of light rays increases).<br> |
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* **interest** : The *total vergence* of several __contiguous thin lenses__ is the *sum of the vergences of each of the lenses* : $`V=\sum V_i`$. |
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or (equivalent) |
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**image focal length** $`f'`$ of the lens : |
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* **positive $`f'`$** ($`f'>0)\:\Longleftrightarrow`$ *focuses light : convergent lens*<br> |
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* **negative $`f'`$** ($`f'<0)\:\Longleftrightarrow`$ *disperse light : divergent lens*<br> |
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* **absolute value of $`f'`$** ($`|f'|`$) : *decreases as the optical phenomenon (focalisation or dispersion) increases*.<br> |
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* **interest** : For thin lenses, the **algebraic value of $f'$** give the *position of the plane* (perpendicular to |
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* the optical axis) and from the lens center *where the image of an object at infinity takes place*. |
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! Nearby in all application, same medium (same refractive index) in both sides of the lens :<br> |
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! $`\Longrightarrow`$ object focal lenght $`f`$ is the opposite of image focal length $`f'`$ : $`f=-f'`$<br> |
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! $`\Longrightarrow`$ only absolute value $`|f'|`$ of $`f'`$ is given, and the lens is specified to be convergeng or divergent. |
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**Relation between vergence (dioptric power), image and object focal lengthes** |
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if the refractive index $`n_{ini}`$ of the medium in which the incident light on the lens propagates, and $`n_{fin}`$ of the medium |
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in which the light emerges from the lens, then : |
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$`V=-\dfrac{n_{ini}}{f}=+\dfrac{n_{fin}}{f'}`$ |
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##### Constitution |
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Piece of **glass, quartz, plastic** (for visible and near infrared and UV).<br> |
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**Rotationally symmetrical**,<br> |
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**Thin**,<br> |
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**2 polished surfaces** perpendicular to its axis of symmetry, **either or both curved** (and most often spherical). |
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##### Classification of thin lenses |
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**Convergent lenses** = **positive lenses** |
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**Divergent lenses** = **negative lenses** |
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### Brief chronology |
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### Modeling a lens |
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##### |
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