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# physics

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- CHAPTER 2 : Geometric Optics
  - Specific objectives
  - Introduction
  - Refraction
  - Reflection
  - Optical Instruments

Content:

## Refraction

### Planar diopter

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

AB :object

A'B' : image

Refraction phenomenon
Refraction phenomenon

- 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 Â = (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)

AB : real object

A'B' : Real ,inverted and enlarged image

AB : real object

A'B' : virtual, Upright, and reduced image

##### 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

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