Incident multi-wavelength mono-ray caustics of rays exiting an isosceles prism, half flanked by a two-ray intersection dihedral space in the form of a Japanese hat

Any multi-wavelength ray refracts producing as many divergent refracted rays as its wavelength content and, consequently, a virtual caustic. The so-called white ray with its continuous wavelength distribution constitutes the most patent case. M. V. Berry, in J. Opt. Soc. Am. A39, C45 (2022)JOAOD60740-323210.1364/JOSAA.474473, is probably the first to have considered such a refractive caustic produced by the emerging rays from a glass prism illuminated by a single ray of white light. On the one hand, he focused on the volume dimensions (hereafter the dihedral flank) delimited by the caustic and the two extreme colored rays of the visible spectrum and, on the other hand, on its inside color distribution, establishing under what conditions it could be observed. Berry speaks of colors and uses approximate formulas partly based on a particular ray incidence angle in order to obtain the <i>k</i>=0 caustic, with k being the number of inside reflections. Here, one uses the refraction index N as an independent variable in the mathematical treatment and deduces exact formulas for <i>k</i>=0 to <i>k</i>=17 caustics (N-caustics), using thereafter the optical relation linking N and wavelength value. Regarding <i>k</i>=0N-caustic and its dihedral flank dimensions, differences with the results in Berry's paper are explained.