In geometric optics, the paraxial approximation is a smallangle 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, namely:^{[1]}
The paraxial approximation is used in Gaussian optics and firstorder ray tracing.^{[1]} Ray transfer matrix analysis is one method that uses the approximation.
In some cases, the secondorder approximation is also called "paraxial". The approximations above for sine and tangent do not change for the "secondorder" paraxial approximation (the second term in their Taylor series expansion is zero), while for cosine the second order approximation is
The secondorder 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.
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Lecture 8: Paraxial Approximation + Small Angle Approximation Lens Makers Equation

26. Physics  Reflection of Light  Paraxial Incident Rays on Spherical Mirrors  Ashish Arora (GA)

Matrix Method in Paraxial Optics
Transcription
References
 ^ ^{a} ^{b} ^{c} ^{d} Greivenkamp, John E. (2004). Field Guide to Geometrical Optics. SPIE Field Guides. 1. SPIE. pp. 19–20. ISBN 0819452947.
 ^ Weisstein, Eric W. (2007). "Paraxial Approximation". ScienceWorld. Wolfram Research. Retrieved 15 January 2014. CS1 maint: discouraged parameter (link)
 ^ "Paraxial approximation error plot". Wolfram Alpha. Wolfram Research. Retrieved 26 August 2014. CS1 maint: discouraged parameter (link)
External links
 Paraxial Approximation and the Mirror by David Schurig, The Wolfram Demonstrations Project.