Geometric optics can be completely derived from Fermat's principle, as classical mechanics can be obtained by the application of the Hamilton principle. In Lagrangian optics, for optical systems with rotational symmetry, is known the invariant L(3), the Lagrange optical invariant. For systems built only with spherical lenses, we demonstrate there are two other optical invariants, L(1) and L(2), analogous to L(3). A proof based on Snell's law, the Weierstrass-Erdman jump condition, and the expression of the ray between two optical surfaces in the Hamiltonian formalism is reported. The presence of a conserved vector, L, allows us to write the equation of an emerging ray without any approximation. (C) 2011 Optical Society of America
Two Lagrange-like optical invariants and some applications
Onorato, Pasquale
2011-01-01
Abstract
Geometric optics can be completely derived from Fermat's principle, as classical mechanics can be obtained by the application of the Hamilton principle. In Lagrangian optics, for optical systems with rotational symmetry, is known the invariant L(3), the Lagrange optical invariant. For systems built only with spherical lenses, we demonstrate there are two other optical invariants, L(1) and L(2), analogous to L(3). A proof based on Snell's law, the Weierstrass-Erdman jump condition, and the expression of the ray between two optical surfaces in the Hamiltonian formalism is reported. The presence of a conserved vector, L, allows us to write the equation of an emerging ray without any approximation. (C) 2011 Optical Society of AmericaI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
