A thin lens is formed by the association of two spherical diopters of large radius of curvature with respect to the thickness of the lens. More precisely, if we denote the radii of curvature. There are two types of lenses:

- lenses with thin edges that are convergent,
- lenses with thick edges that are divergent.
- The different forms of thin lenses
- The different forms of thin lenses.

**Geometric Aberrations**

The **lens edger ** is not a rigorously stigmatic system. The lens is said to have geometric aberrations. The figure below shows that a plano-convex lens gives from point to infinity on the axis a point image provided that its thickness is small in front of its radius of curvature or, what is equivalent, that the rays considered are not very far from the optical axis. It could be shown that it is also necessary that the inclination of the rays be weak.

Geometric Aberrations: simulation of the path of light passing through two convergent plano-convex lenses with the same radius of curvature and different thickness.

**Approximation of Gauss**

The defects of the lenses are observed especially when the rays are very inclined with respect to the optical axis or very far from the optical axis. The Gaussian approximation or the paraxial approximation consists in limiting oneself to little inclined rays and not very far from the optical axis. In this context, we will admit that:

Lenses are stigmatic: the image of a point is a point. This is what allows the formation of images.

The lenses are aplanatic: the image of an object perpendicular to the optical axis is perpendicular to the optical axis.

**Chromatic Aberrations: The path of light rays depends on the wavelength.**

Since the index varies with the wavelength (dispersion phenomenon), the red light will not have the same behavior as the blue light. Thus, in polychromatic light, the image that gives a lens will be iridescent . We then speak of chromatic aberrations. We fight against this defect by adding lenses that compensate for the chromatic dispersion.

**Concept Of Homes**

In the context of the Gaussian approximation, the image of a point is a point. Two points play a special role in lenses: they are object and image focuses .

**Fireplace image**

By definition, the image of a point at infinity on the axis is the focal point F ‘. In the case of a converging lens, the image focus is real while it has the status of virtual image for a divergent lens.

We define the focal length image \ [f ‘\ equiv \ overline {\ text {OF’}} \]

By definition, a luminous object placed at object focus F will have an image at infinity on the axis. In the case of a convergent lens, the object focus is real while it has the status of virtual object for a divergent lens. In a similar way, we define the object focal length \ [f \ equiv \ overline {\ text {OF}} \]

- Object house
- Fireplaces objects.

**To remember**

This relation is obvious for symmetrical lenses (principle of the inverse return of light); in this case O is the center of symmetry of the lens. It is valid for asymmetrical lenses because we place in the approximation of infinitely thin lenses. For a convergent lens,