Abstract
Standard presentations of optics concentrate on ideal systems made for imaging which bring all rays from a point source to one focus. But, in Nature, or in realistic optical systems with defects, rays do not behave precisely in this way. Rather than the focus simply being blurred, the rays, after reflection or refraction, form beautiful and rather universal patterns of bright lines known as caustics. Mathematically speaking, a family of rays is best viewed as a surface in a higher-dimensional space where we keep track of both the position and direction of rays. The intensity enhancement on approaching the caustic line is a singularity, arising from projection of a smooth surface from higher dimensions to lower dimensions. The universal features of such singularities, which arise in many contexts beyond optics, formed a major theme of Vladimir Arnold’s work after 1965, when he was exposed to Rene Thom’s vision of ‘catastrophe theory’. Arnold and his school made seminal contributions to singularity theory.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
