- Paraxial approximation
In

geometric optics , the**paraxial approximation**is anapproximation used in ray tracing of light through an optical system (such as a lens).cite book | first=John E. | last=Greivenkamp | year=2004 | title=Field Guide to Geometrical Optics | publisher=SPIE | others=SPIE Field Guides vol.**FG01**| id=ISBN 0-8194-5294-7 |pages=pp. 19–20 ]A

**paraxial ray**is a ray which makes a small angle ("θ") to theoptical axis of the system, and lies close to the axis throughout the system. Generally, this allows three important approximations (for "θ" inradian s) for calculation of the ray's path::$sin(\; heta)\; approx\; heta$:$an(\; heta)\; approx\; heta$and :$cos(\; heta)\; approx\; 1$

The paraxial approximation is used in "first-order" raytracing and

Gaussian optics .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 are already accurate to second order in "θ", but the approximation for cosine needs to be expanded by including the next term in the

Taylor series expansion. The third approximation then becomes:$cos(\; heta)\; approx\; 1\; -\; \{\; heta^2\; over\; 2\; \}\; .$

The paraxial approximation is fairly accurate for angles under about 10°, but is inaccurate for larger angles.

For larger angles it is often necessary to distinguish between

meridional ray s, which lie in a plane containing theoptical axis , andsagittal ray s, which do not.**References****External links*** [

*http://demonstrations.wolfram.com/ParaxialApproximationAndTheMirror/ Paraxial Approximation and the Mirror*] by David Schurig,The Wolfram Demonstrations Project .

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