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Polarization on Reflection

Polarization on Reflection
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2017-09-26 13:39
TrigonometryComplex NumberGeometric Construction
This example demonstrates the polarization phenomenon of light upon reflection from a surface, dynamically illustrating the relationship between the reflection angle and polarization state. Core mathematical concepts include the law of reflection, linear equations, continuity, rotation, and complex numbers. The construction utilizes GeoGebra commands and objects such as Sequence, Point, Plane, Intersect, Line, and Segment as outlined in the summary. Suitable for high school physics and mathematics education, it combines wave optics with geometric transformations for practical understanding.

GeoGebra Commands & Parameters

  1. Sequence((((2 * sin(θ)) * sin((((2 * π) * f) * t) - i)), i, ((2 * cos(θ)) * sin((((2 * π) * f) * t) - i))), i, -8, 0, 0.2) → list1
  2. Sequence((i, 0, ((2 * cos(θ)) * sin((((2 * π) * f) * t) - i))), i, 0, 10, 0.2) → list2
  3. Point(g) → A
  4. Point(g) → B
  5. Point(zAxis) → C
  6. Point(zAxis) → D
  7. Plane(C, A, D) → b
  8. Point(yAxis) → E
  9. Intersect(zAxis, yAxis) → F
  10. Line(E, F) → j
  11. Intersect(xAxis, j) → G
  12. Point(xAxis) → H
  13. Line(G, H) → k
  14. Segment(G, E) → l
  15. Segment(G, H) → m