Introduction to Nonimaging Optics, 2nd Edition

15

Rays and Wavefronts

15.1 Optical Momentum

The optical momentum vector p at a point Q on a light ray is tangent to the light ray at that point Q. We will now see that p is also perpendicular to the surfaces S = constant and, therefore, these surfaces are perpendicular to the light rays.

For the Lagrangian L=L(x1,x2,x3,x1′,x2′) used in Equation 14.51 we can write

Considering the Euler Equation 14.52, we get¹

and therefore,

Considering