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.
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.