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Figure 3
Examples of solutions of the Cartesian oval equation (18)[link] at various values of [n^{\prime}/n] for a representative set of values for q1 (23.0929 m) and q2 (8.6912 m). The solutions `y(x)' were calculated by using the exact equations (38)[link] and (39)[link] for [x \,\gt\, 0]; note that y( - x) = y(x). The solutions `x(y)' were calculated by solving equation (18)[link] as a quadratic equation in x2 with y-dependent coefficients [see equation (45)[link]]. The top row demonstrates three cases in which [n^{\prime}/n \,\gt\, 1] and the bottom row demonstrates three cases in which [n^{\prime}/n \,\lt\, 1]. In each row, [n^{\prime}/n \to 1] from left to right. The sheet labelled `surface of lens' is the one that fulfills the original lens equation (12)[link].

Journal logoJOURNAL OF
SYNCHROTRON
RADIATION
ISSN: 1600-5775
Volume 24| Part 6| November 2017| Pages 1120-1136
https://doi.org/10.1107/S1600577517011808
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