Rainbow Software

In Kinshasa, many companies offer consumers mineral water packaged in plastic bottles. The packaging of the latter gives them prestigious consideration. Unfortunately, these waters exposed to the sun by sellers create health concerns for consumers through the release of toxic chemical compounds. This study focused on the antimony contamination of mineral water put into PET plastic bottles sold in Kinshasa. The samples consist of bottles of mineral water (American Water, Alpina, Eden, and Swissta), purchased in the markets of the city province of Kinshasa, sent and analyzed to the water and environmental chemistry laboratory of the Faculty of Science and Technology of the University of Kinshasa. The general objective of this work is to verify whether water put in plastic bottles (PET) exposed to the sun (to heat) contains or can release antimony. To achieve the results, we used the experimental method, which consisted of collecting mineral water samples and analyzing them before and after their exposure to the sun. Laboratory results revealed the presence of antimony in mineral waters before and after exposure to the sun, exceeding the WHO reference value (6 μg/l). There was also a release of this element into the water, exponentially increasing the initial values. A good monitoring and control policy for marketed food products and environmental education of sellers as well as that of the population are effective measures to recommend to preserve the health of consumers. IndexTerms-Mineral water, antimony, PET plastic bottle, endocrine disruptor.

The focusing problem of lenses is examined and especially Descartes Ovals. A connection with Sahl's lens is examined. If the source of light is on the left of the sahle lens all rhe rays inside the lens are parallel. We examine a rotated Sahl lens and how to find the right side so thetotal optic length to be cosnstant

In teaching about waves the students are learning how to find the refracted rays by using wave fronts or finding the wave fronts by using the rays. The usual teaching is based on models where the speed of the wave is constant in one medium and changes abruptly as the wave passes from one medium to another. This paper deals with ways of calculation the wave fronts and the rays for the case of a continuous changing of the index of refraction. For this purpose, Fermat's principle is applied for multiple layers of very small thickness. Two models are presented for the speed of the waves: A model on which the wave speed depends on the square root of the depth of penetration of the wave and the other model, where the speed depends on a linear dependence. In both cases it is found that as the wave progresses it is "totally reflected". In the case of the "square root dependence" the solution is a kind of cycloid which shows this behavior. In the linear case it is found that there is a moment where the wave is reflected, which is found by the maximum of a quantity "Z". By using this quantity, the coordinates x and y can be calculated. As an application the refraction of the light in the atmosphere is calculated, where the dependence of the distance from the center of the earth is calculated and again the 2 models are applied. In this case the "square root" model gives a stronger deviation from the linear model. This helps the student to understand the change on the perceived position of the celestial bodies.

The paper examines ways of teaching wave pulses traveling on strings and wave fronts in two dimensional waves. The phenomena examined for pulses are: reflection, transmission and superposition. Two methods of finding the refracted wave fronts, the corresponding rays and the refraction angle are presented. Then the gradual change of the speed of propagation of a wave is presented. In the last part is examined the application of the concept of wave fronts in lenses and Huygens’ method of finding the shape of a perfect lens. The students’ difficulties with connection with all these subjects are presented.

Abstract Water management and design of irrigation and drainage projects are based on extreme values rather than on average values. Annual daily maximum rainfall corresponding to return periods varying from 2 to 100 years is used by design engineers and hydrologists for economic planning, and design of minor and major hydraulic structures. This research aims at performing frequency analysis of annual daily maximum rainfall in Amman- Zarqa Basin (AZB) which is an important basin in Jordan. Daily rainfall data at 22 stations distributed in Amman-Zarqa Basin with long time series (more than 40 years) were used for this purpose. For each station, the annual 1- day maximum rainfall data were extracted. Daily maximum values have then been statistically analyzed by RAINBOW software using two probability distribution functions, namely: Linear and log normal distributions. The goodness of fit for the selected distributions is tested using the Chi-square and the Kolmogorov–Simrnov tests at th...

Abstract Water management and design of irrigation and drainage projects are based on extreme values rather than on average values. Annual daily maximum rainfall corresponding to return periods varying from 2 to 100 years is used by design engineers and hydrologists for economic planning, and design of minor and major hydraulic structures. This research aims at performing frequency analysis of annual daily maximum rainfall in Amman- Zarqa Basin (AZB) which is an important basin in Jordan. Daily rainfall data at 22 stations distributed in Amman-Zarqa Basin with long time series (more than 40 years) were used for this purpose. For each station, the annual 1- day maximum rainfall data were extracted. Daily maximum values have then been statistically analyzed by RAINBOW software using two probability distribution functions, namely: Linear and log normal distributions. The goodness of fit for the selected distributions is tested using the Chi-square and the Kolmogorov–Simrnov tests at th...

We present mathematics for the construction of presentations using Excel for Ibn Sahl's lens and also Huygen's lens. These methods are based onf Fermat's principle. Huygen's lens can have a spherical frontal surface of a Hyperbolic one. Sahl has both surfaces hyperbolic. This is an advantage in the calculation of the Caustics

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

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.

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.  We also examine the Huygens Lens and the Ibn Sahl 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 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

In this paper, the inclusion of history and philosophy of science in science teaching is proposed with the goal of depicting pre-service primary teachers' perception of the role of historical experiments in learning science and the nature of science. In order to achieve this, a teaching-learning sequence was designed and conducted in the context of an Introductory Physics Laboratory Course following the integrated approach to teaching the nature of science. Ptolemy's experiments on refraction and the combination of his advanced and erroneous views contributed to pre-service primary teachers' conceptualization of the empirical and tentative nature of science and the relationship between mathematics and science. The majority of the pre-service primary teachers perceived the history of science as important in understanding scientific concepts and aspects of the nature of science.

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.