Excel Files for Teaching Caustics of Rainbow and Lenses

In this paper, Software is presented for teaching through interactive demonstrations about caustics on rainbows and lenses. At first we explore the caustics on rainbows since they are amenable to analytic calculations. We find 4 kinds of caustics: 2 internal (of first refraction and reflection) and 2 external (second refraction and exciting from the back of the drop, and 2 nd refraction emerging on the front). We examine caustics of lenses constructed by two spherical surfaces. We explore the ray diagrams and wave fronts and give methods for finding the caustics. We also examine the case of thick lens and the caustics due to reflection A spreadsheet is in https://www.researchgate.net/publication/344523149_SPHERICAL_LENS_and_reflection_CAUSTICS?_sg=k2qyMymlM5ZrvYac4dJEbOCVRfXQZ5zV_KjJjF0OfFkmv3JCKIkXrrb7iwEDiWI6zo35MtUWgmxXlrNBeTVgdJ8d5LY9u4NLmHlfpPW3.00aIFUH7PbeX8oXUEJMZ257tgE8MKcpXkfrwqH5elj9MA6V-L9J6MTOEABwq4TlB4nLAMpYvy3o7Ep1EmSghsQ

The paper examines different ways of using historical resources in teaching refraction related subjects. Experimental procedures can be taught by using Ptolemy’s and Al Haytham’s methods. The student can check the validity of the approximations or rules which were presented by different people. The interpretation of the relations is another subject. Refraction phenomena were interpreted either by the principle of least time or by particles or by waves. The law of refraction can be used as an example of a law which was discovered but put aside. The use of the law to construct lenses can be seen in Ibn Sahl’s hyperbolical lenses. Al Farisi’s method of ‘‘cones’’ is used for the interpretation of the rainbow. Al Farisi’s model was discovered again by Descartes. These models were not able to explain the supernumerary arcs. For this reason a simple wave model is presented. The models proposed by Al Haytham of atmospheric refraction can be used to show that refraction actually cannot be considered as the cause of the change of the size of the moon. Finally Huygens model of refraction in the atmosphere is used to introduce the wave fronts as more fundamental than rays.

Applied Optics

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European Journal of Physics, 1997

Incoherent averaging over orientations of refracted beams of rays can generate a 'fake caustic', namely an intensity pattern with a geometrical singularity identical to that of a caustic produced by focusing of a family of rays (i.e. its envelope). However, the diffraction at a fake caustic is very different from the Airy fringes near a genuine caustic. We calculate this unusual type of diffraction and demonstrate its existence experimentally with a rotating prism. Zusammenfassung. Inkoherente Mittelungüber die Orientierungen von gebrochenen Strahlenbündeln kann eine 'falsche Kaustik' erzeugen, nämlich ein Intensitätsmuster mit einer geometrischen Singularität identisch zu der einer Kaustik, die durch Fokusierung einer Familie von Strahlen (d.h. ihre Einhuellende) hervorgebracht wurde. Die Beugung in einer falschen Kaustik aber ist sehr verschieden von den Airy Streifen nahe einer echten Kaustik. Wir berechnen diesen ungewöhnlichen Typ einer Beugung und zeigen ihre Existenz experimentell mit einem rotierenden Prisma.

Journal of Mathematical Sciences and Modelling

One can often see caustic by reflection in nature but it is rather hard to understand the way of how caustic arise and which geometric properties of a mirror surface define geometry of the caustic. The caustic by reflection has complicated topology and much more complicated geometry. From engineering point of view the geometry of caustic by reflection is important for antenna's theory because it can be considered as a surface of concentration of the reflected wave front. In this paper we give purely geometric description of the caustics of wave front (flat or spherical) after reflection from mirror surface. The description clarifies the dependence of caustic on geometrical characteristics of a surface and allows rather simple and fast computer visualization of the caustics in dependence of location of the rays source or direction of the pencil of parallel rays.

Applied Optics, 1994

Oblate drops of water can produce caustics where, unlike a simple Airy caustic, more than two rays merge. We extend previous treatments of generalized primary rainbows based on catastrophe optics [Opt. Lett. 10, 588 (1985); Proc. R. Soc. (London) A 438, 397 (1992)] to rays having (p-1) = 2 to 5 internal reflections. The analysis is for a horizontally illuminated ellipsoid with a vertical symmetry axis. Aspect ratios causing a vanishing of the vertical curvature at the equator for the outgoing wave front are found from generalized ray tracing. In response to infinitesimal deformation, the axial caustic of real glory rays unfolds producing cusps. Laboratory observations with laser illumination demonstrate that cusps resulting from rays with five internal reflections extend into Alexander's dark band when the drop's aspect ratio is near 1.08. The evolution of this p = 6 scattering pattern as cusps meet the quinary rainbow is suggestive of an E 6 catastrophe. For ellipsoids of varying aspect ratio and refractive index N, there is an organizing singularity associated with an exceptionally flat outgoing wave front from spheres with N = p.

IEEE EDUCON 2010 Conference, 2010

Optical systems may be complex to study, especially when they involve media with spatially varying refractive index. A fast, accurate and easy to use MATLAB code for solving the iconal equation in such media is presented. It is used for ray-tracing the propagation of light in non-homogeneous media and illustrating some amazing effects in modern physics that cannot be brought to the attention of students without the aid of numerical simulations.

The paper examines different ways of using historical resources in teaching refrac-tion related subjects. Experimental procedures can be taught by using Ptolemy " s and AlHay-tham " s methods. The student can check the validity of the approximations or rules whichv were presented by different people. The interpretation of the relations is another subject Re-fraction phenomena were interpreted either by the principle of least time or by particles or by waves. The law of refraction can be used as an example of a law which was discovered but put aside. The use of the law to construct lenses can be seen in Ibn Sahl " s hyperbolical lenses. Al Farisi " s method of " " cones " " is used for the interpretation of the rainbow. Al Farisi " s model was discovered again by Descartes. These models were not able to explain the supernumerary arcs. For this reason a simple wave model is presented. The models proposed by Al Haytham of atmospheric refraction can be used to show that refraction actually cannot be considered as the cause of the change of the size of the moon. Finally Huygens model of refraction in the atmosphere is used to introduce the wave fronts as more fundamental than rays.

Optik, 2018

This paper is concerned with one of the most common atmospheric optical phenomenonthe rainbow. In order to get rid of the ambiguity present in the traditional theory of formation of rainbow which is based on the traditional ambiguous angles of incidence, reflection, and refraction, a novel unambiguous theory of formation of rainbow which makes use of the refined unambiguous angles of incidence, reflection, and refraction has been offered. As a result, the present contribution will enhance and sophisticate the relevant optical physics literature there by enriching the same as well.

2018

This chapter extends Part III of the book From Photon to Neuron (Princeton Univ Press 2017). This preliminary version is made freely available as-is in the hope that it will be useful.