A sphere of radius a whose refractive index at radius r is n(r) = (2a/r − 1)1/2 for r < a (with n = 1 for r > a) is shown to be a perfect ‘retrorefractor’ in geometrical optics; every ray incident on the sphere is bent through 180°. This compares favourably with a conventional retroreflector of three circular mirrors intersecting at right angles (eight corner reflectors) which retroreflects only one-seventh of all incident rays. However, the retrorefracting sphere suffers serious impracticalities.
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Hannay et al. (1993) studied this question.