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[[File:Small angle compare error.svg|thumbnail|The error associated with the paraxial approximation. In this plot the cosine is approximated by {{nowrap|1 - θ<sup>2</sup>/2}}.]]
In [[geometric optics]], the '''paraxial approximation''' is a [[small-angle approximation]] used in [[Gaussian optics]] and [[Ray tracing (physics)|ray tracing]] of light through an optical system (such as a [[lens (optics)|lens]]).<ref name="Greivenkamp">{{Cite book | isbn = 0-8194-5294-7 | title = Field Guide to Geometrical Optics | last1 = Greivenkamp | first1 = John E. | year = 2004 | publisher = [[SPIE]] | series = SPIE Field Guides | volume = 1 | page = <!-- can't have both --> | pages = 19–20 <!-- --> }}</ref>
<ref>{{cite web
| last=[[Eric W. Weisstein|Weisstein]]
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| work=[[ScienceWorld]]
| publisher=[[Wolfram Research]]
| accessdate=15 January 2014|year=2007}}</ref>
A '''paraxial ray''' is a [[Ray (optics)|ray]] which makes a small angle (''θ'') to the [[optical axis]] of the system, and lies close to the axis throughout the system.<ref name=Greivenkamp/> Generally, this allows three important approximations (for ''θ'' in [[radian]]s) for calculation of the ray's path:<ref name=Greivenkamp/>
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