# Paraxial approximation

In geometric optics, the **paraxial approximation** is a small-angle approximation used in Gaussian optics and ray tracing of light through an optical system (such as a lens).^{[1]}
^{[2]}

A **paraxial ray** is a ray which makes a small angle (*θ*) to the optical axis of the system, and lies close to the axis throughout the system.^{[1]} Generally, this allows three important approximations (for *θ* in radians) for calculation of the ray's path:^{[1]}

and

The paraxial approximation is used in Gaussian optics and *first-order* ray tracing.^{[1]} Ray transfer matrix analysis is one method that uses the approximation.

In some cases, the second-order approximation is also called "paraxial". The approximations above for sine and tangent do not change for the "second-order" paraxial approximation (the second term in their Taylor series expansion is zero), while for cosine the second order approximation is

The second-order approximation is accurate within 0.5% for angles under about 10°, but its inaccuracy grows significantly for larger angles.^{[3]}

For larger angles it is often necessary to distinguish between meridional rays, which lie in a plane containing the optical axis, and sagittal rays, which do not.

## References

- ↑
^{1.0}^{1.1}^{1.2}^{1.3}Template:Cite isbn - ↑ Template:Cite web
- ↑ Template:Cite web

## External links

- Paraxial Approximation and the Mirror by David Schurig, The Wolfram Demonstrations Project.