In optics the Lagrange invariant is a measure of the light propagating through an optical system. It is defined by
,
where y and u are the marginal ray height and angle respectively, and ȳ and ū are the chief ray height and angle. n is the ambient refractive index. In order to reduce confusion with other quantities, the symbol Ж may be used in place of H.[1]Ж2 is proportional to the throughput of the optical system (related to étendue).[1] For a given optical system, the Lagrange invariant is a constant throughout all space, that is, it is invariant upon refraction and transfer.
The optical invariant is a generalization of the Lagrange invariant which is formed using the ray heights and angles of any two rays. For these rays, the optical invariant is a constant throughout all space.[2]
lagrange, invariant, optics, measure, light, propagating, through, optical, system, defined, displaystyle, overline, overline, where, marginal, height, angle, respectively, chief, height, angle, ambient, refractive, index, order, reduce, confusion, with, other. In optics the Lagrange invariant is a measure of the light propagating through an optical system It is defined by H n u y n u y displaystyle H n overline u y nu overline y where y and u are the marginal ray height and angle respectively and ȳ and u are the chief ray height and angle n is the ambient refractive index In order to reduce confusion with other quantities the symbol Zh may be used in place of H 1 Zh2 is proportional to the throughput of the optical system related to etendue 1 For a given optical system the Lagrange invariant is a constant throughout all space that is it is invariant upon refraction and transfer The optical invariant is a generalization of the Lagrange invariant which is formed using the ray heights and angles of any two rays For these rays the optical invariant is a constant throughout all space 2 See also editEtendue Smith Helmholtz invariant Abbe sine conditionReferences edit a b Greivenkamp John E 2004 Field Guide to Geometrical Optics SPIE Field Guides vol FG01 SPIE p 28 ISBN 0 8194 5294 7 Optics Fundamentals Newport Corporation retrieved 9 8 2011 nbsp This optics related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Lagrange invariant amp oldid 1080056808, wikipedia, wiki, book, books, library,
