optical invariant

The optical invariant, also known as the Lagrange invariant or Smith-Helmholtz invariant, is a fundamental concept in geometrical optics. It represents the product of the object height (h), the refractive index of the medium (n), and the paraxial ray angle (u). This product (hnu) remains constant throughout a lens system, regardless of its complexity.1

This invariant is crucial for determining the magnification of an optical system, which is the ratio of the image size to the object size. By knowing the initial object's quantities and tracing a paraxial ray, one can calculate the image height. This principle is essential for understanding how lenses form images and is a cornerstone of optical design.1