Lens (optics) divergence of a collimated beam, it does alter the width of the beam. The magnification of such a telescope is given by which is the ratio of the output beam width to the input beam width. Note the sign convention: a telescope with two convex lenses ("f" > 0, "f" > 0) produces a negative magnification, indicating an inverted image. A convex plus a concave lens ("f" > 0 > "f") produces a positive magnification and the image is upright. For further information on simple optical telescopes, see Refracting telescope § Refracting telescope designs. Cylindrical lenses have curvature in only
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