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Reflection off Round Surface

Reflection off Round Surface
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2015-10-16 23:02
CircleVectorTrigonometryCalculusGeometric Construction
This example demonstrates the reflection of light off a round surface, dynamically showing the relationship between the angle of incidence and reflection. It involves core mathematical concepts such as the law of reflection, derivatives, trigonometric functions, vectors, and geometric transformations. The construction uses GeoGebra commands like Circle, Tangent, OrthogonalLine, Vector, Mirror, Segment, Intersect, and Angle. Suitable for high school and above students studying geometric optics, calculus, and trigonometric applications, or for physics teaching.

GeoGebra Commands & Parameters

  1. Circle(B, C) → c
  2. Tangent(C, c) → a,
  3. OrthogonalLine(C, a) → b
  4. Vector(A, C) → u
  5. Mirror(A, b) → A'
  6. Vector(C, A') → v
  7. Segment(A, A') → d
  8. Intersect(b, d) → D
  9. Angle(A, C, D) → α
  10. Angle(D, C, A') → β