William Herschel (1706-1761) tried to correct for this distortion by combining two separate lenses, but it was still difficult to achieve good resolution for far distant light sources. Reflector telescopes, invented by Isaac Newton in 1668, used a single concave mirror rather than a convex lens. The concave mirror gathered more light than a lens, reflecting it onto a flat mirror at the end of the telescope for viewing. A smaller mirror could provide greater magnification and a larger field of view than a convex lens. Newton's first mirror was 1.3 inches in diameter; such mirrors were rarely more than 3 inches
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