paraxialtilnærmingen

The paraxial approximation is a simplification used in optics and other fields to describe the behavior of light rays or other wave phenomena that travel close to a principal axis. This approximation is valid when the angle of the ray with respect to the axis is small. In this regime, trigonometric functions of the angle can be approximated by the angle itself, for example, sin(θ) ≈ θ and cos(θ) ≈ 1.

This simplification is crucial for deriving many fundamental equations in geometric optics, such as the lens maker's equation and the thin lens equation. These equations allow for the prediction of image formation by lenses and mirrors. The paraxial approximation assumes that light rays are confined to a narrow region around the optical axis and do not deviate significantly from it.

Beyond basic optics, the paraxial approximation also finds application in areas like charged particle beams in accelerators and wave propagation in waveguides. The validity of the approximation depends on the specific geometry and the degree of deviation from the principal axis. When rays deviate substantially, non-paraxial effects become significant, and more complex mathematical treatments are required.