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Reflection of Light on a Parabola

Reflection of Light on a Parabola
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2018-06-07 13:21
FunctionCoordinate GeometryCalculusDerivative
This example demonstrates the reflection of light on a parabola, illustrating key mathematical concepts such as parabolas, reflection laws, differential calculus, and coordinate geometry. It is constructed using GeoGebra commands like Sequence, Point, CurveCartesian, and lists (리스트1-7), along with buttons (버튼1-3). Ideal for high school students and math enthusiasts exploring parabolic optics and calculus applications.

GeoGebra Commands & Parameters

  1. Sequence(x = (a / n * (((t - 1) * 2) + 1)) - a, t, 1, n) → 리스트1
  2. Sequence(Intersect[c, Element[리스트1, t]], t, 1, n) → 리스트2
  3. Sequence(Tangent[Element[리스트2, t], c], t, 1, n) → 리스트3
  4. Sequence(Intersect[f, Element[리스트1, t]], t, 1, n) → 리스트4
  5. Sequence(CurveCartesian[(a / n * (((t - 1) * 2) + 1)) - a, b - w, w, 0, If[v < b - y(Element[리스트2, t]), v, b - y(Element[리스트2, t])]], t, 1, n) → 리스트5
  6. Sequence(CurveCartesian[(a / n * (((t - 1) * 2) + 1)) - a, b - w, w, b - y(Element[리스트2, t]), v], t, 1, n) → 리스트6
  7. Sequence(Mirror[Element[리스트6, t], Element[리스트3, t]], t, 1, n) → 리스트7
  8. Point(c) → A
  9. CurveCartesian(u, u^(2), u, x(A), (-x(A))) → d