拉格朗日不变量是光学系统中对于光传播的量测，定义为

其中y和u为边缘光线的高度及角度，而ȳ及ū为主光线的高度及角度。n为环境的折射率。为了不要和别的物理量混淆，有时会用符号Ж来代替H。 Ж和光学系统的通量成正比（和光学扩展量有关）。对于一光学系统，拉格朗日不变量在所有的空间中均为不变量，因此在折射及光传播后，拉格朗日不变量都不会改变。

光学不变量（optical invariant）是拉格朗日不变量的延伸，利用二个光线的高度及角度计算而得。对这些光线而言，光学不变量在所有空间中都是定值。

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. Ж is proportional to the throughput of the optical system (related to étendue). For a given optical system, the Lagrange invariant is a constant throughout all space, that is, it is invariant upon refraction and transfer.