Paraxial approximation: Difference between revisions

Revision as of 02:14, 10 September 2010

Revision as of 00:43, 13 November 2010

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The paraxial approximation is used in ''first-order'' raytracing and [[Gaussian optics]].<ref name=Greivenkamp/> [[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 toTo second order in ''θ'', but the approximationapproximations above for cosinesine needsand totangent bedo expandednot by includingchange (the next term in thetheir [[Taylor series]] expansion. Theis thirdzero), approximationwhile for cosine thenthe second approximation becomes

:<math> \cos(\theta) \approx 1 - { \theta^2 \over 2 } \ .</math>