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. Generally, this allows three important approximations (for θ in radians) for calculation of the ray's path, namely:
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.
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- Weisstein, Eric W. (2007). "Paraxial Approximation". ScienceWorld. Wolfram Research. Retrieved 15 January 2014.
- "Paraxial approximation error plot". Wolfram Alpha. Wolfram Research. Retrieved 26 August 2014.