Lens (optics) is the focal length of the lens, which is commonly abbreviated "f" in diagrams and equations. An extended hemispherical lens is a special type of plano-convex lens, in which the lens's curved surface is a full hemisphere and the lens is much thicker than the radius of curvature. If the lens is biconcave or plano-concave, a collimated beam of light passing through the lens is diverged (spread); the lens is thus called a "negative" or "diverging" lens. The beam, after passing through the lens, appears to emanate from a particular point on the axis in front of the lens. The
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