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Excel Files for Teaching About Wave Fronts and Rays for a Wave Moving in Media with Changing Index of Refraction

Received: 10 August 2021     Accepted: 20 August 2021     Published: 27 August 2021
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Abstract

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.

Published in American Journal of Physics and Applications (Volume 9, Issue 4)
DOI 10.11648/j.ajpa.20210904.14
Page(s) 94-101
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Rays, Wave Front, Snell’ Law, Total Reflection

References
[1] Halloun, I. (2018). Scientific Models and Modeling in the Framework of Systemic Cognition and Education. Working paper. Jounieh, LB: H Institute.
[2] Sunil Kumar Katoch, (2020) “MS-Excel Spreadsheet Applications in Introductory Under-Graduate Physics-A Review”, Journal of Science and Technology, Vol. 05, Issue 03, May-June 2020, pp48-52.
[3] Pavlos Mihas (2017) Excel Files for Teaching Two Dimensional Motions and their Curvature, Global Journal of Science Frontier Research: I Interdisciplinary vol. 16.3GJSFR (2016) Volume 16 Issue 3: 23-32 January 2017 DOI: 10.17406/GJSFRIVOL16IS3PG23.
[4] Pavlos Mihas (2020) Original Paper, Excel Files for Newton's Proposition V, May 2020, Applied Science and Innovative Research 4 (2): 41-52 DOI: 10.22158/asir.v4n2p41.
[5] Manuel I González (2018) Lens ray diagrams, Phys. Educ. 53 03501.
[6] Pavlos Mihas (2019) Software for Teaching through Interactive Demonstrations about Converging Lenses, Applied Science and Innovative Research (Online) Vol. 3, No. 1, 2019 www.scholink.org/ojs/index.php/asir.
[7] Pavlos Mihas (2021) Excel Files for Teaching Caustics of Rainbow and Lenses (spherical, Huygens and Ibn Sahl) in Journal of Physics & Optics Sciences. SRC/JPSOS/147 March 2021 DOI: 10.47363/JPSOS/2021(3)13.
[8] Mila Kryjevskaia, MacKenzie R. Stetzer, and Paula HR. L. Heron (2012) Student understanding of wave behavior at a boundary: The relationships among wavelength, propagation speed, and frequency, American Journal of Physics80 (4), April 2012.
[9] Tutorials in Introductory Physics by Peter S. Shaffer McDermott, Lillian C | Jan 1, 2012.
[10] Pavlos Mihas & Triantafyllos Gemousakakis (2020) Teaching about waves with applications in lenses, Journal of Education and Social studies, Vol. 2,2 pp 38-52.
[11] G. Polya (1954) Induction and Analogy in Mathematics, Vol. 1 Princeton University Press.
[12] Leonid Minkin & Percy Whitning (2019) Restricted Brachistochrone, The Physics Teacher 57, 359.
[13] Brian S. Blais (2020) Model Comparison in the introductory Laboratory, The Physics Teacher 58, 209.
[14] Michael Nauenberg (2017) Newton's theory of the atmospheric refraction of light American Journal of Physics 85, 921 (2017).
[15] W. J. Humphreys (1920) Physics of the Air THE FRANKLIN INSTITUTE OF THE STATE OF PENNSYLVANIA By J. B. LIPPINCOTT COMPANY, 2012 printing by FORGOTTEN BOOKS www.forgottenbooks.org.
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  • APA Style

    Pavlos Mihas. (2021). Excel Files for Teaching About Wave Fronts and Rays for a Wave Moving in Media with Changing Index of Refraction. American Journal of Physics and Applications, 9(4), 94-101. https://doi.org/10.11648/j.ajpa.20210904.14

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    ACS Style

    Pavlos Mihas. Excel Files for Teaching About Wave Fronts and Rays for a Wave Moving in Media with Changing Index of Refraction. Am. J. Phys. Appl. 2021, 9(4), 94-101. doi: 10.11648/j.ajpa.20210904.14

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    AMA Style

    Pavlos Mihas. Excel Files for Teaching About Wave Fronts and Rays for a Wave Moving in Media with Changing Index of Refraction. Am J Phys Appl. 2021;9(4):94-101. doi: 10.11648/j.ajpa.20210904.14

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  • @article{10.11648/j.ajpa.20210904.14,
      author = {Pavlos Mihas},
      title = {Excel Files for Teaching About Wave Fronts and Rays for a Wave Moving in Media with Changing Index of Refraction},
      journal = {American Journal of Physics and Applications},
      volume = {9},
      number = {4},
      pages = {94-101},
      doi = {10.11648/j.ajpa.20210904.14},
      url = {https://doi.org/10.11648/j.ajpa.20210904.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20210904.14},
      abstract = {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.},
     year = {2021}
    }
    

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    AU  - Pavlos Mihas
    Y1  - 2021/08/27
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    N1  - https://doi.org/10.11648/j.ajpa.20210904.14
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    JF  - American Journal of Physics and Applications
    JO  - American Journal of Physics and Applications
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    EP  - 101
    PB  - Science Publishing Group
    SN  - 2330-4308
    UR  - https://doi.org/10.11648/j.ajpa.20210904.14
    AB  - 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.
    VL  - 9
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Author Information
  • The Department of Primary Education, School of Education, Democritus University of Thrace, Alexandroupolis, Greece

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