Plano-convex ingot Plano-convex ingot Plano-convex ingots are lumps of metal with a flat or slightly concave top and a convex base. They are sometimes, misleadingly, referred to as bun ingots which imply the opposite orientation of concavity. They are most often made of copper although plano-convex ingots of other materials such as copper alloy, lead and tin are also known. Plano convex ingots are found across a wide chronological and geographical range with the first examples known from the Near East during the 3rd and 2nd Millennia BC. By the end of the Bronze Age they were found throughout Europe and in
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