Light patterns generated by the reflected rays

Journal of the Optical Society of America A, 2013

The aim of the present work is twofold: first we obtain analytical expressions for both the wavefronts and the caustic associated with the light rays reflected by a spherical mirror after being emitted by a point light source located at an arbitrary position in free space, and second, we describe, in detail, the structure of the ronchigrams when the grating or Ronchi ruling is placed at different relative positions to the caustic region and the point light source is located on and off the optical axis. We find that, in general, the caustic has two branches: one is a segment of a line, and the other is a two-dimensional surface. The wavefronts, at the caustic region, have self intersections and singularities. The ronchigrams exhibit closed-loop fringes when the grating is placed at the caustic region.

2009

The Gaussian formula and spherical aberrations of the static and relativistic curved mirrors are analyzed using the optical path length (OPL) and Fermat's principle. The geometrical figures generated by the rotation of conic sections about their symmetry axes are considered for the shapes of the mirrors. By comparing the results in static and relativistic cases, it is shown that the

In this article there is investigated the character of the singularities' distribution corresponding to the analytical continuation of the field reflected by the front part of the perfect electric conductor sphere illuminated by the electromagnetic waves point source. The analysis of these singularities show, that they represent the distorted image of the incident wave source and are distributed on the caustic surface. The discrete character of the singularities, when the ratio of the sphere radius and the incident wave length is finite, is explained by the Fresnel zone method. The numerical experiments performed to determine the scattered field's singularities confirm theoretical reasoning based on geometrical optics and Fresnel's zone method.

Journal of Optics, 2011

The Gaussian formula and spherical aberrations of the static and relativistic curved mirrors are analyzed using the optical path length (OPL) and Fermat's principle. The geometrical figures generated by the rotation of conic sections about their symmetry axes are considered for the shapes of the mirrors. By comparing the results in static and relativistic cases, it is shown that the focal lengths and the spherical aberration relations of the relativistic mirrors obey the Lorentz contraction. Further analysis of the spherical aberrations for both static and relativistic cases have resulted in the information about the limits for the paraxial approximation, as well as for the minimum speed of the systems to reduce the spherical aberrations.

1999

In computer graphics, it is often an advantage to calculate reflections directly, especially when the application is time-critical or when line graphics have to be displayed. We specify formulas and parametric equations for the reflection on spheres and cylinders of revolution. The manifold of all reflected rays is the normal congruence of an algebraic surface of order four. Their catacaustic surfaces are given explicitly. The calculation of the reflex of a space point leads to an algebraic equation of order four. The up to four practical solutions are calculated exactly and efficiently. The generation of reflexes of straight lines is optimized. Finally, reflexes of polygons are investigated, especially their possible overlappings. Such reflexes are the key for the reflection of polyhedra and curved surfaces. We describe in detail how to display their contours.

2020

Euler used intrinsic equations expressing the radius of curvature as a function of the angle of inclination to find curves similar to their evolutes. We interpret the evolute of a plane curve optically, as the caustic (envelope) of light rays normal to it, and study the Euler's problem for general caustics. The resulting curves are characterized when the rays are at a constant angle to the curve, generalizing the case of evolutes. Aside from analogs of classical solutions we encounter some new types of curves. We also consider caustics of parallel rays reflected by a curved mirror, where Euler's problem leads to a novel pantograph equation, and describe its analytic solutions.

The development of the modern world is accelerating thanks to many scientific achievements of physics that are being applied in our technological fields. The optic fibers for example contributed in deploying the internet networks around the world and are considered the main current application of light in technologies. However, quantum devices are still considered not ready to be widely used by ordinary consumers, because studying the light has always been a very difficult task. Optics researches started from ancient philosophical and theological works and are still being developed by famous physics scientists as the main subject of their quantum physics experiments that can’t neglect even the principles of Einstein’s Relativity. And thus, motivated by the appearance of my previous article about the light in the very useful Book titled the "Worldwide List of Alternative Theories and Critics (edition 2023)", I proposed an experiment similar to Sagnac-disk by using moving concave mirrors in order to trap light beams in a rotating environment. I presented in this work the related formulas and I could even guess some recurrence relations if the trapped Light-Beam is reflected several times from the moving wall of mirrors. However, the work exposes a contradiction concerning the reflected light beams velocity vectors and this makes us suspect the correctness of some formulas of light reflection when dealing with concave mirrors. The aim of this article is to propose an experiment that can be very interesting since it can expose an interesting effect of the rotating mirrors on the light. The methodology of the developed formulae is simplified by using mathematical and geometric demonstrations without needing any complicated results from the background of other published articles. However, the observed contradictions about concave mirrors that are exposed in this article should be studied experimentally in order to deduce the correct formulas before performing the experiment of the disk of rotating concave mirrors in the laboratories. Hence, this is a basis that would make this interesting experiment succeed in order to observe all the effects of moving concave mirrors on the light.

Physics 310 them. The path is called a ray of light, and a bundle of such rays constitutes a beam of light.

Chaos: An Interdisciplinary Journal of Nonlinear Science

We study the formation of images in a reflective sphere in three configurations using caustics on the field of light rays. The optical wavefront emerging from a source point reaching a subject following passage through the optical system is, in general, a Gaussian surface with partial focus along the two principal directions of the Gaussian surface; i.e., there are two images of the source point, each with partial focus. As the source point moves, the images move on two surfaces, referred to as viewable surfaces. In our systems, one viewable surface consists of points with radial focus and the other consists of points with azimuthal focus. The problems we study are (1) imaging of a parallel beam of light, (2) imaging of the infinite viewed from a location outside the sphere, and (3) imaging of a planar object viewed through the point of its intersection with the radial line normal to the plane. We verify the existence of two images experimentally and show that the distance between t...

Resonance, 2012

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. "Classroom" is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science.