@ -62,23 +62,44 @@ refracting interface corresponds to two different plane refracting surfaces :<br
!!!! \- refracting index of the medium of the emergent light : $n_{eme} = n_{water} = 1.33$.
!!!!
####
!!!! *BE CAREFUL* :<br>
!!!! In the same way as we use in English the single word "mirror" to qualify a "reflecting surface", in French is use the single word "dioptre" to qualify a "refracting surface".
!!!! The term "dioptre" in English is a unit of mesure of the vergence of an optical system. In French, the same unit of measure is named "dioptrie".
!!!! _A crystal ball forms a spherical refracting surface : un "dioptre sphérique" in French._
!!!!
!!!! unit of measure : *EN : dioptre* , *ES : dioptría* , *FR : dioptrie*.<br>
!!!! _My corrective lens for both eyes are 4 dioptres : "4 dioptries" in French._
#### Non stigmatism of spherical refracting surfaces
Ray tracing study of a **spherical refracting surface** :
[Click here for geogebra animation](https://www.geogebra.org/material/iframe/id/zqwazusz)<br>
* **At each impact point** of the rays upon the spherical refracting surface, the **Snell-Descartes relation applies**.
<br>
Fig. 3. : In each point of the spherical refracting surface, the Snell-Descartes relation applies.
* A spherical refracting surface is **not stigmatic** : The *rays (or their extensions)* originating *from a same object point* and that emerge from the surfac egenerally *do not converge towards an image point*.
<br>
Fig. 4. : A spherical refracting surface is not stigmatic: The rays (or their extensions) coming
from an object point generally do not converge towards an image point.
<br>
Fig. 5a. : If we limit the opening of the spherical refracting surface so that only the rays
* **If we limit the opening** of the spherical refracting surface so that only the rays
meeting the surface near the vertex are refracted through the surface.
<br>
* **and if** the object points remain close enough to the optical axis, so that the **angles of
incidence and refraction remain small**, then for each object point an image point can be almost
defined, and therefore the spherical refracting surface becomes *quasi-stigmatic*.
<br>
Fig. 5b. : and if the object points remain close to the optical axis, so that the angles of
incidence and refraction remain small, then for each object point an image point can be almost
defined, and therefore the spherical refracting surface becomes quasi-stigmatic.
#### Gauss conditions / paraxial approximation and quasi-stigmatism
@ -92,68 +113,27 @@ $`sin(\alpha) \approx tan (\alpha) \approx \alpha`$, and $`cos(\alpha) \approx
*Geometrical optics limited to Gaussian conditions* is called *Gaussian optics* or *paraxial optics*.
#### Characterization of a spherical refracting surface
* 2 distincts points : **vextex S** and **center of curvature C** on the optical axis,
which defines $`\overline{SC}`$ : algebraic distance between vertex S and center C of curvature on optical axis.
* 2 refractive index values :<br>
\- **$`n-{inc} : refractive index of the medium of the incident light**.<br>
\- **$`n-{eme} : refractive index of the medium of the emergent light**.
* 1 arrow : indicates the *direction of light propagation*
#### Thin spherical refracting surface
We call **thin spherical refracting surface** a spherical refracting surface *used in the Gauss conditions*.
#### Analytical study (in paraxial optics)
spherical refracting surface
!!!! DIFFICULT POINT:<br>
!!!! A same plane or spherical plane refracting interface will have two different optical behaviors, will be modeled by two different sets of parameters, depending on the direction of the light propagation.
!!!!
!!!! Consider a plane interface (a thick window whose thickness and effect can be neglected) that separates air and water, and two twins (Thompson and Thomson) at equal distances on both sides of the interface.
!!!!
!!!! <!-- fig 2a to add --><br>
!!!! Fig. 2a. The situation is not symmetrical :
!!!!
!!!! * When Thompson (in air) looks at Thomson (in water) the light propagets from Thomson to Thompson's eyes. The fact is that Thompson sees the image of his brother closer than the real position of his brother.
!!!!
!!!! <!-- fig 2b to add--><br>
!!!! Fig. 2b.
!!!
!!!! * In the opposite situation, when Thomson (in water) looks at his brother (in air), the light propagates from Thompson to Thomson's eyes. And the fact is that Thomson sees the image of his brother farther away from his real position.<br>
!!!! (Strictly speaking, the eye of a fish should be considered in this situation, eyes well adapted to vision in water and in direct contact with water. If not, we should consider that the Thomson's dive mask is filled with water, to have Thomson's eyes in contact with water and not to add another water/air refracting surface (that of the dive mask) on the path of the light rays :
!!!!
!!!! <!-- fig 2c to add-→<br>
!!!! Fig. 2c.
!!!!
!!!! All this can be predicted and calculated, but this example shows that this air/water plane refracting interface corresponds to two different plane refracting surfaces :
!!!!
!!!! * First case : refracting surface such as :<br>
!!!! \- refractive index of the medium of incident light : $n_{inc}=n_{water}=1.33$<br>
!!!! \- refractive index of the medium of emerging light : $n_{eme}=n_{air}=1$
!!!!
!!!! * Second case : for this refracting surface :<br>
!!!! \- refractive index of the medium of incident light : $n_{inc}=n_{air}=1$<br>
!!!! \- refractive index of the medium of emerging light : $n_{eme}=n_{water}=1.33$
!!!!
### How is modeled in paraxial optics ?
#### Characterization of a spherical refracting surface
* 2 distincts points : **vextex S** and **center of curvature C** on the optical axis,
which defines $`\overline{SC}`$ : algebraic distance between vertex S and center C of curvature on optical axis.
* 2 refractive index values :<br>
\- **$`n-{inc} : refractive index of the medium of the incident light**.<br>
\- **$`n-{eme} : refractive index of the medium of the emergent light**.
* 1 arrow : indicates the *direction of light propagation*
