Lens (optics) in the accompanying diagrams), while "negative" "R" means that rays reaching the surface have already passed the center of curvature. Consequently, for external lens surfaces as diagrammed above, and indicate "convex" surfaces (used to converge light in a positive lens), while and indicate "concave" surfaces. The reciprocal of the radius of curvature is called the curvature. A flat surface has zero curvature, and its radius of curvature is infinity. If "d" is small compared to "R" and "R", then the "thin lens" approximation can be made. For a lens in air, "f" is then given by As mentioned above, a
Luneburg lens one side, and formula_14 only on the other: The parameter formula_19 is a constant for any given ray, but differs between rays passing at different distances from the centre of the lens. For rays passing through the centre, it is zero. In some special cases, such as for Maxwell's fish-eye, this first order equation can be further integrated to give a formula for formula_14 as a function or formula_13. In general it provides the relative rates of change of formula_14 and formula_13, which may be integrated numerically to follow the path of the ray through the lens. Luneburg lens A