scholarly journals Excel Files for Teaching Caustics of Rainbow and Lenses

2021 ◽  
pp. 1-7
Author(s):  
Pavlos Mihas ◽  
Keyword(s):  
Wave Fronts ◽  
Spherical Surfaces ◽  
Thick Lens

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 externals (second refraction and exciting from the back of the drop, and 2nd 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

scholarly journals Software for Teaching through Interactive Demonstrations about Converging Lenses

2019 ◽  
Vol 3 (1) ◽  
pp. 15
Author(s):  
Pavlos Mihas
Keyword(s):  
Graphical Representation ◽  
Focal Length ◽  
Least Square ◽  
Image Point ◽  
Focal Distance ◽  
Spherical Surfaces ◽  
Step Procedure ◽  
Linear Fit ◽  
Principal Points ◽  
Thick Lens

<p><em>In this paper, Software is presented for teaching through interactive demonstrations about lenses. At first we explore lenses constructed by two spherical surfaces. We explore the ray diagrams and wave fronts. Then there is a page for understanding the thick lens model. We introduce a step by step procedure to find the focal length and find the principal planes and finally the use of the focal length and principal points to construct the image. There is a page for finding the position of the image not by the formula but by the method we use on an actual experiment: We move the screen back and forth until we can get the sharpest possible image. This is done by finding the minimum of a standard deviation of the position of the rays for a given position of the screen. Then there is a simulation of an experiment for finding the focal length. This uses a macro to simulate the finding of several image points b for several object points a. These values are used first in the graphical representation of the image point as a function of b and the image points as a function of a. With suitable least square fits we get two lines with parameters that give values for the focal length and principal plane. Then there is a simulation of two experiments of finding the focal length of a lens. The spreadsheet calculates the distance b vs a, the image y, and there ar graphs of y as a function of a and y as a function of b from which we find 1) a hyperbolic fit for y vs a and a linear fit for y vs b from which we calculate the focal distance, 2) it calculates 1/a and 1/b and then finds a linear fit and a parabolic fit for the data. Also we get the same parameters by finding the cuts of lines uniting the point (a,0) and (0,b).. 3) there is a plot of a+b vs a and then the points are fitted with a hyperbola whose asymptotes give the sum of focal length and principal planes. Then there is a page where we can see two lenses for which the shape can change to have a perfect focusing at a given distance. These two lenses are based on Huygens’ ideas, Spherical and Huygen Lenses.</em></p>

On the matter of proving Euclidean fifth postulate and the origin of non-Euclidean geometries

2019 ◽  
Vol 950 (8) ◽  
pp. 2-11
Author(s):  
S.A. Tolchelnikova ◽  
K.N. Naumov
Keyword(s):  
Celestial Mechanics ◽  
Natural Philosophy ◽  
Relativity Theory ◽  
Theory Of Relativity ◽  
The Third ◽  
Stellar Astronomy ◽  
Spherical Surfaces ◽  
Mathematical System ◽  
Solar System Bodies ◽  
The Universe

The Euclidean geometry was developed as a mathematical system due to generalizing thousands years of measurements on the plane and spherical surfaces. The development of celestial mechanics and stellar astronomy confirmed its validity as mathematical principles of natural philosophy, in particular for studying the Solar System bodies’ and Galaxy stars motions. In the non-Euclidean geometries by Lobachevsky and Riemann, the third axiom of modern geometry manuals is substituted. We show that the third axiom of these manuals is a corollary of the Fifth Euclidean postulate. The idea of spherical, Riemannian space of the Universe and local curvatures of space, depending on body mass, was inculcated into celestial mechanics, astronomy and geodesy along with the theory of relativity. The mathematical apparatus of the relativity theory was created from immeasurable quantities

scholarly journals Controlling wave fronts with tunable disordered non-Hermitian multilayers

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Denis V. Novitsky ◽  
Dmitry Lyakhov ◽  
Dominik Michels ◽  
Dmitrii Redka ◽  
Alexander A. Pavlov ◽  
...  
Keyword(s):  
Incident Light ◽  
Passage Time ◽  
Photonic Devices ◽  
Gain Saturation ◽  
Wave Fronts ◽  
Optical Effects ◽  
Front Shape ◽  
Optical Applications ◽  
Increasing Demand ◽  
First Time

AbstractUnique and flexible properties of non-Hermitian photonic systems attract ever-increasing attention via delivering a whole bunch of novel optical effects and allowing for efficient tuning light-matter interactions on nano- and microscales. Together with an increasing demand for the fast and spatially compact methods of light governing, this peculiar approach paves a broad avenue to novel optical applications. Here, unifying the approaches of disordered metamaterials and non-Hermitian photonics, we propose a conceptually new and simple architecture driven by disordered loss-gain multilayers and, therefore, providing a powerful tool to control both the passage time and the wave-front shape of incident light with different switching times. For the first time we show the possibility to switch on and off kink formation by changing the level of disorder in the case of adiabatically raising wave fronts. At the same time, we deliver flexible tuning of the output intensity by using the nonlinear effect of loss and gain saturation. Since the disorder strength in our system can be conveniently controlled with the power of the external pump, our approach can be considered as a basis for different active photonic devices.

Testing the link between mergers and AGN in the Arp 245 system

2020 ◽  
Vol 15 (S359) ◽  
pp. 192-194
Author(s):  
Elismar Lösch ◽  
Daniel Ruschel-Dutra
Keyword(s):  
Star Formation ◽  
Active Galactic Nucleus ◽  
Spherical Surface ◽  
Galaxy Mergers ◽  
Nuclear Activity ◽  
Upper Limit ◽  
Spherical Surfaces ◽  
Galactic Centers ◽  
Merger Event ◽  
Major Merger

AbstractGalaxy mergers are known to drive an inflow of gas towards galactic centers, potentia- lly leading to both star formation and nuclear activity. In this work we aim to study how a major merger event in the ARP 245 system is linked with the triggering of an active galactic nucleus (AGN) in the NGC galaxy 2992. We employed three galaxy collision numerical simulations and calculated the inflow of gas through four different concentric spherical surfaces around the galactic centers, estimating an upper limit for the luminosity of an AGN being fed the amount of gas crossing the innermost spherical surface. We found that these simulations predict reasonable gas inflow rates when compared with the observed AGN luminosity in NGC 2992.

scholarly journals Numerical and theoretical modeling of droplet impact on spherical surfaces

2021 ◽  
Vol 33 (5) ◽  
pp. 052112
Author(s):  
Hussein N. Dalgamoni ◽  
Xin Yong
Keyword(s):  
Droplet Impact ◽  
Theoretical Modeling ◽  
Spherical Surfaces

High-order harmonic wave fronts generated with controlled astigmatic infrared laser

2008 ◽  
Vol 25 (7) ◽  
pp. B161 ◽  
Author(s):  
Constance Valentin ◽  
Julien Gautier ◽  
Jean-Philippe Goddet ◽  
Christoph Hauri ◽  
Tatiana Marchenko ◽  
...  
Keyword(s):  
Harmonic Wave ◽  
Infrared Laser ◽  
High Order ◽  
Wave Fronts ◽  
High Order Harmonic

scholarly journals Wave Fronts in a Causality-Violating Gödel-Type Metric

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Thomas P. Kling ◽  
Faizuddin Ahmed ◽  
Megan Lalumiere
Keyword(s):  
Wave Front ◽  
Space Time ◽  
Wave Fronts ◽  
Light Rays ◽  
Synchronized Clocks

The light rays and wave fronts in a linear class of the Gödel-type metric are examined to reveal the causality-violating features of the space-time. Noncausal features demonstrated by the development of unusual wave front singularities are shown to be related to the nonmonotonic advance of time along the light rays, as measured by a system of observers at rest with respect to one another with synchronized clocks.

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