We construct an optical lens in the (x, y)-plane which focuses two pairs of points, i.e., all the rays from a given point X i are focused by the lens at a given point y i , for i = 1, 2. The points X 1, X 2, Y 1, Y 2 lie on the x-axis and the lens has the form
where γ 1, γ 2 are given, and f i (0) = 0, f i (−y) = f i (y). We then let X 2 → X 1, Y 2 → Y 1 and investigate the limiting lens. We show that this limit is generally not a symmetric lens, i.e., f 1 + f 2 ≇ 0.
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Friedman, A., McLeod, B. An optical lens for focusing two pairs of points. Arch. Rational Mech. Anal. 101, 57–83 (1988). https://doi.org/10.1007/BF00281783
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