Light diffraction from a quantum approach: a proposal for secondary school

Authors

  • María de los Angeles Fanaro
  • Marcelo Arlego

DOI:

https://doi.org/10.55767/2451.6007.v30.n1.20319

Keywords:

Light diffraction, Quantum approach, Didactic sequence, Secondary school

Abstract

Light diffraction phenomenon can be approached from different viewpoints depending on whether one seeks to describe the final result or the process of forming of that result; each of them with a model that allows to describe and predict the phenomenon. In this paper we propose a way to approach the light diffraction from the quantum perspective that adopts the Feynman approach, as a reference to make it teachable to high school students. Although the original method "Feynman's Path Integral" is complex, it is possible to apply it to the experiment of light diffraction in a simple way, based on geometrical-vectorial considerations, as is presented in the first part of this work. In the second part, we present the result of the work of didactic transposition in the sense of Chevallard, as a proposal to bring up the quantum concepts of probability and superposition. Our didactic proposal is based on the Theory of Conceptual Fields of Vergnaud, reason why the design of the sit-uations is the key for the conceptualization of the students. From this perspective, we present and describe the situations and simulations made with spreadsheets, as a calculation and visualization tool.

References

Chevallard, Y. (1997) [1985].La transposición didáctica. Del saber sabio al saber enseñado. Buenos Aires: Aique.

Clement, J. (2009). The Role of Imagistic Simulation in Scientific Thought Experiments. Topics in Cog-nitive Science,1(4), 686–710.

Colin, P. y Viennot, L. (2001). Using two models in optics: Students’ difficulties and suggestions for teaching. American Journal of Physics, 69(7), S36.

Dobson, K., Lawrence, I. y Britton, P. (2006). The A to B of quantum physics. Physics Education, (35)6.

Dowrick, N. J. (1997). Feynman’s sum–over–histories in elementary quantum mechanics. European Journal of Physics,18, 75–78.

Fanaro, M. y Otero, M. R. (2008).Basics Quantum Mechanics teaching in Secondary School: One Con-ceptual Structure based on Paths Integrals Method.Lat. Am. J. Phys. Educ., 2(2), 103–12.

Fanaro, M., Otero, M. R. y Arlego, M. (2009).Teaching the foundations of quantum mechanics in secon-dary school: a proposed conceptual structure.Investigações em Ensino de Ciências, 14(1), 37–64.

Fanaro, M., Arlego, M. y Otero, M. R. (2012).A Didactic Proposed for Teaching the Concepts of Electrons and Light in Secondary School Using Feynman´s Path Sum Method. European Journal of Physics Education, 3(2), 1–11.

Fanaro, M., Otero, M. R. y Arlego, M. (2012a).A proposal to teach the light at secondary school from the Feynman method. Problems of Education in the 21st Century, 47(47), 27–39.

Fanaro, M., Otero, M. R. y Arlego, M. (2012b).Teaching Basic Quantum Mechanics in Secondary School Using Concepts of Feynman’s Path Integrals Method. The Physics Teacher, (50), 156–158.

Fanaro M., Arlego, M. y Otero, M. R. (2014).The double slit experience with light from the point of view of Feynman's sum of multiple paths.Rev. Bras. Ensino Fís., 36(2), 1–7.

Fanaro, M., Elgue, M. y Otero, M. (2016). Secuencia para enseñar conceptos acerca de la luz desde el enfoque de Feynman para la mecánica cuántica en la escuela secundaria: un análisis basado en la teoría de los campos conceptuales. Caderno Brasileiro de Ensino de Física., 33(2), 477–506.

Fanaro, M., Arlego, M., Elgue, M. y Otero, M. R. (2017).The students´ interpretation of quantum me-chanics concepts from the Feynman´s Sum of All Paths applied to light. International Journal of Physics and Chemistry Education. [En prensa]

Feynman, R. (1985).QED The strange theory of light and matter. EEUU: Penguin Books– Princeton University Press.

Feynman, R. y Hibbs. A. (1965).Quantum Mechanics and Path Integrals. Mc Graw–Hill.

Feynman, R., Leighton, R. y Sands, M. (1987).Física Vol. 1. EEUU:Adison–Wesley Iberoamericana.

Gilbert, J.K.y Reiner, M. (2000).Thought experiments in science education: potential and current realiza-tion. International Journal of Science Education, 22(3), 265–283.

Gitin, A. (2013).Huygens–Feynman–Fresnel principle as the basis of applied optics. Applied optics Opti-cal Society of America, 52(31), 7419–7434.

Halliday, D., Resnick, R. y Walker, J.(2011).Fundamentals of Physics. 9th Ed.EEUU: John Wiley & Sons.

Hanc, J. y Tuleja, S. (2005).The Feynman quantum mechanics with the help of Java applets and physlets in Slovakia. Proccedings of the 10th Workshop on Multimedia in Physics Teaching and Learning, Freie Universität Berlin.

Hetch, E. (2000).Óptica. 3ra Ed. Madrid: Addison Wesley Iberoamericana.

Malgieri, M., Onorato, P. y De Ambrosis, A. (2014).Teaching quantum physics by the sum over paths approach and GeoGebra simulations. European Journal of Physics, 35, 055024 (21pp.).

Malgieri, M., Onorato, P. y De Ambrosis, A. (2015).What is Light? From Optics to Quantum Physics Through the Sum over Paths Approach.Teaching/Learning Physics Integrating research into practice GIREP–MPTL 2014 Conference Proceedings,639–646.Disponible en: http://www1.unipa.it/girep2014/item6.html (consultado en febrero de2018).

Malgieri, M., Onorato, P. y De Ambrosis, A. (2017). Test on the effectiveness of the sum over paths ap-proach in favoring the construction of an integrated knowledge of quantum physics in high school. Phys-ics Review Physics Education Resources, 13, 019901.

Maurines, L. (2010). Geometrical Reasoning in Wave Situations: The case of light diffraction and coher-ent illumination optical imaging. International Journal of Science Education, 32(14), 1895–1926.

Michelini, M., Stefanel, A. y Santi, L. (2003).Teacher training strategies on physical optics: experimenting the proposal on diffraction. Quality Development in Teacher Education and Training Second Interna-tional GIREP. Udine, Italia. 568–576.

Ogborn, J., Hanc, J. y Taylor, E. (2006). A First Introduction to Quantum Behavior.Proceedings The GIREP Conference 2006, Modeling in Physics and Physics Education.AMSTEL Institute, Amsterdam. p. 213.

Otero, M.R., Fanaro, M., Sureda, P., LLanos, V. C. y Arlego, M. (2014).La teoría de los campos concep-tuales y la conceptualización en el aula de matemática y física. Buenos Aires: Dunken.

Ramil, A., López, A. J., y Vincitorio, F. (2007).Improvements in the analysis of diffraction phenomena by means of digital images. American Jounal of Physics, 75, 999.

Stefanel, A. (1997). Un’esperienza sul campo di introduzione della fisica quantistica nella scuola secon-daria superiore. La Fisica nella Scuola, XXX, 3 Supplemento, Q7, 58–67.

Taylor, E., Stamatis Vokos, J., O’Meara, M.y Thornber, N. (1998).Teaching Feynman’s Sum Over Paths Quantum Theory.Computers in Physics, 12, 190–199.

Vergnaud, G. (1990). La teoría de los campos conceptuales. Recherches en Didáctique des Mathema-tiques, 10(23), 133–170.

Wosilait, K., Heron, P. R. L., Schaffer, P. S., y Mc Dermott, L. (1999). Addressing students’ difficulties in applying a wave model to the interference and diffraction of light. Physics Education Research: A supplement to the American Journal of Physics, 67(7), 5–15.

Wua, X.Y., Zhang, B.J., Yang, J.H., Chia, L.X., Liua, X.J., Wua, Y.H., Wanga, Q.C., Wanga, Y., Lib, J.W., y Guoc, Y.Q. (2010). Quantum theory of light diffraction. Journal of Modern Optics, 57(20), 2082–2091.

Published

2018-06-22

How to Cite

Fanaro, M. de los A., & Arlego, M. (2018). Light diffraction from a quantum approach: a proposal for secondary school. Journal of Physics Teaching, 30(1), 63–74. https://doi.org/10.55767/2451.6007.v30.n1.20319