5. Conclusion

In this article, the approximation of geometrical optics has enabled two approaches to emerge, the first leading to Descartes' laws and the second highlighting the scope of caustics.

Illustrated by catadioptric systems, catacaustics (reflection caustics) led naturally to conjugation relations linking object and image position for cylindrical or spherical mirrors, imposing the single-point constraint. Descartes' laws, on the other hand, are applied to dioptric systems such as plane diopters, spherical diopters or variable-index media.

Light guidance is then discussed from a wide-angle perspective, illustrated by the spherical defects of plano-convex lenses. The need to restrict ourselves to paraxial optics is demonstrated, to preserve the stigmatism and aplanatism of optical systems, and also to demonstrate the usefulness of matrix optics....