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A Ray in a Corner

A Ray in a Corner
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2014-06-25 02:58
AngleVectorTrigonometryGeometric Construction
In collections Light
This example demonstrates the path of a ray of light caught between two infinite, intersecting mirrors. It illustrates the reflection phenomenon, involving core math concepts like the law of reflection, angles, vectors, and geometric constructions. Constructed using GeoGebra commands such as Circle, Point, Vector, Line, Ray, Angle2, Angle, Arc1b, Sequence, Zip, Append, PolyLine, SegmentLabel1. Suitable for high school students learning about geometric reflections and vector concepts.

GeoGebra Commands & Parameters

  1. Circle(A, 1) → c
  2. Point(c) → B
  3. Vector(A, B) → u0
  4. Line(A, B) → a
  5. Ray(A, B) → l1
  6. Point(c) → C
  7. Vector(A, C) → u1
  8. Line(A, C) → b
  9. Angle2(B, A, C) → α
  10. Angle(B, A, C) → α''
  11. Point(l1) → X0
  12. Angle(X0 + u0, X0, X0 + n0) → β
  13. Arc1b(X0, X0 + u0, X0 - u0, σ) → g
  14. Point(g) → L
  15. Vector(X0, L) → R0
  16. Arc1b(X0, X0 + u0, L, σ) → θ
  17. Angle(aux1 + u1, aux1, aux1 + n1) → γ
  18. Sequence(k, k, 0, m) → ki
  19. Zip(floor(k / 2), k, ki) → ck
  20. Zip(ceil(k / 2), k, ki) → dk
  21. Zip(Mod[ki + 1, 2], ki, ki) → k1
  22. Zip((zθ * k1) + (zθ' * k2), k1, k1, k2, k2) → ζθ
  23. Zip((zn0 * k1) + (zn0' * k2), k1, k1, k2, k2) → η0
  24. Zip((zn1' * k1) + (zn1 * k2), k1, k1, k2, k2) → η1
  25. Zip(Vector[((z * p^(c)) * q^(d))], z, dk, ζθ, p, η0, c, ck, q, η1, d) → Rk
  26. Append(t0, Sequence[tm / ((Element[Rk, k] * Element[nrm, Mod[k, 2] + 1])), k, 1, m - 1]) → times
  27. Zip(A + (t * Element[{u0, u1}, Mod[k, 2] + 1]), t, times, k, ki) → Xk
  28. Zip(Vector[Xk, Xk + Rk], Xk, Xk, Vector[Rk], Rk) → Resultants
  29. Ray(Element[Xk, m], Vector[Element[Rk, m]]) → rayEnd
  30. PolyLine(Xk) → rayPath
  31. SegmentLabel1(A, X0, -0.2, 0.15, 0.05, 0.05, 0.5) → pLBL_t, lbl_t

AI Drawing Prompt Reference

Draw two intersecting lines forming a corner, representing two mirrors meeting at a point. Place a unit circle centered at the intersection, with two points on the circle defining the mirror directions. From a point on one mirror, emit a ray that reflects repeatedly between the two mirrors, creating a polyline path. Each segment's direction follows the law of reflection, with angles marked. Show the complete reflected ray path and the final outgoing ray direction.
The prompt above was compiled from the original drawing commands and is for reference only.