In
optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of optical instruments, instruments that use or Photodetector, detect it. Optics usually describes t ...
the Lagrange invariant is a measure of the light propagating through an optical system. It is defined by
:
,
where and are the
marginal ray height and angle respectively, and and are the
chief ray
In optics, a ray is an idealized geometrical model of light or other electromagnetic radiation, obtained by choosing a curve that is perpendicular to the ''wavefronts'' of the actual light, and that points in the direction of energy flow. Rays ...
height and angle. is the ambient
refractive index
In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refrac ...
. In order to reduce confusion with other quantities, the symbol may be used in place of .
is proportional to the throughput of the optical system (related to
étendue
Etendue or étendue (; ) is a property of light in an optical system, which characterizes how "spread out" the light is in area and angle. It corresponds to the beam parameter product (BPP) in Gaussian beam optics. Other names for etendue include ...
).
[ For a given optical system, the Lagrange invariant is a constant throughout all space, that is, it is invariant upon ]refraction
In physics, refraction is the redirection of a wave as it passes from one transmission medium, medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commo ...
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.Optics Fundamentals
, Newport Corporation, retrieved 9/8/2011
See also
*
Etendue
Etendue or étendue (; ) is a property of light in an optical system, which characterizes how "spread out" the light is in area and angle. It corresponds to the beam parameter product (BPP) in Gaussian beam optics. Other names for etendue inclu ...
*
Smith-Helmholtz invariant
*
Abbe sine condition
References
{{Optics-stub
Geometrical optics