Mestrado Profissional em Matemática em Rede Nacional (PROFMAT-SJC)

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Navegando Mestrado Profissional em Matemática em Rede Nacional (PROFMAT-SJC) por Autor "Oliveira, Arthur Alves De [UNIFESP]"

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    Proposta didática para o ensino interdisciplinar: Óptica Geométrica e Matrizes
    (Universidade Federal de São Paulo (UNIFESP), 2020-07-31) Oliveira, Arthur Alves De [UNIFESP]; Sakamoto, Kelly Cristina Jorge [UNIFESP]; Universidade Federal de São Paulo
    Light and its behavior have always been the subject of several studies and much discussion, until it has been concluded that light can have a wavy and corpuscular behavior (particles), which characterizes the theory of wave-particle duality. Various optical phenomena can occur from the interaction of light with matter, such as refraction, reflection, diffraction, absorption, among others. What scientists have observed is that depending on the phenomenon and the ease of better understanding, one can choose whether to explain it, using light as a wave or as a particle. For example, by the wave theory, it is possible to understand the diffraction effect that light suffers when passing through a crack (an obstruction) using the Huygens Principle, and well demonstrated by Young's double-slit experiment. Another example is when light strikes the surface of a mirror, which, in this case, can be treated as a particle and as a wave. In the situation where the size of the opening through which the light beam is propagated, it is much larger compared to the wavelength of the light used, the diffraction effect can be neglected and thus, geometric optics can be applied. In this case, ray tracing and geometry tools are used to determine the parameters that make up the optical image system, such as the distances of the object and image planes in relation to the lens position and the sizes of the object in these planes. The didactic proposal of this work explores the formation of image by an optical system, composed of one or more lenses using four different forms, utilizing the algebraic form by using the lens equation; the geometric shape through the ray tracing; in a matrix form by the application of transfer matrices and the last form with practical classes, experimentally setting up the optical system. In this way, this proposal relates geometric optics (image formation) and matrices to be an interdisciplinary teaching of Physics and Mathematics. Several authors defend the interdisciplinarity in the teaching of Mathematics and Physics, for connecting these contents and showing a real application of Mathematics. In addition, the use of practical activities interferes in the teaching of Physics, as the student can visualize and understand a content that appears, in most cases, abstract. Therefore, it is expected that teaching together both concepts can offer contextualization in class, improvements in student learning and teacher satisfaction, reaping the positive results of their work.