Light patterns generated by the reflected rays

Ates F., Ekmekci F. N.

OPTIK, vol.224, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 224
  • Publication Date: 2020
  • Doi Number: 10.1016/j.ijleo.2020.165507
  • Journal Name: OPTIK
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, INSPEC
  • Keywords: Spherical curve, Spherical orthotomic curve, Spherical caustic curve, Singularity
  • Ankara University Affiliated: Yes

Abstract

In this study, we investigate the special curve that is formed by the reflection of the light rays emitted from the point light source on the unit sphere from a spherical curved mirror. Also, spherical caustic curves are defined as the geometrical location of the focusing requests of the reflected light rays. To examine the trajectories of the light rays emitted from the point light source, we are using the Sabban frame apparatus of the spherical curved mirror on the sphere. Also, the contact points of these curves are examined in terms of the Sabban frame apparatus. Then, the singularity conditions of these curves are examined and the shapes in which they are diffeomorphic are characterized. Finally, we give an example, which is an application of our theorems and definitions, and we visualized the shapes of curved mirrors and point light source in the example with the help of Mathematica program.