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Fig. 1

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Shapes of obstacles: (a) For each isosceles triangle, the point force (directed along the x2 axis) is located at the center of gravity of the triangle and the density outside the triangle is ten times larger than inside the triangle. Moreover, starting from this equilateral triangle of base 20 cm, and a height H equal to cm, we have built three isosceles triangles keeping always the same base of 20 cm but increasing each time the height H as follows: four-thirds of H for the first isosceles triangle, five-thirds of H for the second isosceles triangle, and six-thirds of H for the last isosceles triangle. (b) A convex lens (of maximum half-width H) with a point force (directed along the x2 axis) above it. (c) A layered Luneburg lens (a disk surrounded by 10 concentric layers) with a point force (directed along x1) on its left side. The density of disk, layers, and the surrounding medium, appears on the color scale (in units of 103 kg.m−1).

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