Refraction
Planar diopter
Two transparent media separated by a flat surface. The flat surface is the plane diopter

AB :object
A'B' : image



Conjugate Formula
It is the relationship between the object position, image position, and the characteristics of the optical system.

The parallel-faced blade
Medium with refractive index n confined by two parallel planes


The direction of the emerging ray is independent of the index of the blade; the incident and emerging rays are parallel if the extreme media are identical.
Prism
Definition:
A prism is a set of three transparent, homogeneous, and isotropic media separated by two flat diopters. The flat diopters are, in practice, limited to segments AB and AC and form a triangle in a cutting plane or main section plane. The angle  = (AB, AC) is called the apex angle.
If n is the index of the prism, Snell-Descartes laws at I and I' impose the following two relations.

Total deviation
• Diopter (air-prism) :

• Diopter (prism-air) :


The total deviation :


To see the video click here
Spherical diopter
A spherical diopter is a spherical surface with center C separating two media with different refractive indices. It is characterized by the vertex, the center, and the optical axis that passes through S and C.

Conjugate Formula

With: V is the vergence or the power of the diopter (unit: δ = Diopter = m⁻¹)
If V > 0: Converging diopter
If V < 0: Diverging diopter
The magnification

𝜸>0: Upright image
𝜸 <0 : Inverted image
|γ|<1: Reduced image
|γ| >1: Enlarged image
Foci
Object focus F: the point on the axis that corresponds to an image at infinity; SF is the object focal distance.

An incident ray passing through the object focus of the lens will refract into a ray parallel to the optical axis of the dioper
Image focus F': the point on the image axis of an object point located at infinity; SF' is the image focal distance.

It follows from this definition that any incident ray parallel to the optical axis refracts through the image focus F'.
Image struction:
Concave spherical diopter ((SC)< 0)
Convex spherical diopter ((S C )> 0).


AB : real object
A'B' : virtual, Upright, and reduced image


AB : real object
A'B' : real, inverted and reduced image
We will use three specific rays for this construction :
• A ray originating from B and passing through the object focal point F: it is refracted along a line parallel to the principal axis.
• A ray passing through the center of the lens, which is not deviated upon passing through it.
• A ray originating from B and parallel to the principal axis: it is refracted along a line that passes through the image focal point.
Thin lenses
The different types of lenses
There are two families of lenses:
1. Lenses with thin edges, they are convergent.
2. Lenses with thick edges, they are divergent.

The conjugate focal formula

Magnification 𝜸

𝜸>0: Upright image
𝜸 <0: Inverted image
|γ|<1: Reduced image
|γ| >1: Enlarged image
Vergence :
V=1/f ́ (Unit : V in Dioptres 𝜹 : 1𝜹=m⁻¹
Image formation
Ray construction : the construction of the image of an extended object obeys the following
rules:
We will place ourselves in the Gaussian approximation : stigmatism and planetism approximated.
To find the image of a point, simply consider two rays coming from this point.
The image of a point on the optical axis is also on the optical axis
If the object is real, it is necessarily to the left of the lens.
If the object is virtual, it is located to the right of the lens.
A horizontal ray arriving at a lens will converge at F' if it is convergent and will diverge appearing to come from F' if the lens is divergent.
A ray passing or extending at F will emerge horizontally.
A ray passing through O is not deflected.
Once the rays have been traced, we determine whether the image is real or virtual.
Convergent lenses: C. L :f ́>0


Divergent lenses C. L :f ́<0

