Understanding the Paraxial Approximation
The paraxial approximation (approximation at small angles) is a useful mathematical trick for doing ray tracing and simplifying optical calculations. It assumes that angular deviations in propagation from a beam axis are minimal, and is a key part of the optical designer’s toolbox, especially when it comes to laser physics and fiber optics.
But it’s important to check and double-check to be sure that this approximation is valid for your optical system. While this approximation works well for many small angles, it becomes more and more problematic as ray angles increase. If you utilize the paraxial approximation where it doesn’t apply you may end up with a system that performs very differently in practice than it did on paper.
The paraxial approximation leads to minimal errors in many applications, but there are other situations in which the error ends up being very large.