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Total Internal Reflection Demonstration

Total Internal Reflection Demonstration
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2020-08-02 23:13
AngleVectorGeometric Construction
This example demonstrates the graphical phenomenon of total internal reflection at an interface. It involves core mathematical concepts such as the law of reflection, Snell's law, critical angle, angle calculation, vectors, and geometric transformations. The construction utilizes GeoGebra commands and objects like Mirror, Intersect, Ray, Angle, Rotate, Point, Vector, Line, Segment, and Textfield as outlined in the summary. It is suitable for high school physics optics teaching and analytical geometry learning, helping students visualize and understand the principles and calculations of total internal reflection.

GeoGebra Commands & Parameters

  1. Mirror(B, yAxis) → B'
  2. Intersect(xAxis, yAxis) → A
  3. Mirror(A, yAxis) → A'_1
  4. Ray(A'_1, B') → f'
  5. Ray(A, B) → f
  6. Angle(yAxis, f') → r_{2}
  7. Ray(A, C) → g
  8. Rotate(A, r, (0, 0)) → A'
  9. Rotate(C, (-r), (0, 0)) → C'
  10. Ray(A', C') → g'
  11. Angle(g', g) → r_{1}
  12. Ray(A'_1, B') → h
  13. Point(f) → D
  14. Vector(B, D) → u
  15. Point(f') → G
  16. Intersect(r_{2}, f, 1) → H
  17. Intersect(f, h) → I
  18. Point(h) → J
  19. Vector(I, J) → a
  20. Intersect(f, h) → L
  21. Point(h) → M
  22. Vector(L, M) → w
  23. Intersect(f, g') → E
  24. Point(g') → F
  25. Vector(E, F) → v
  26. Point(yAxis) → K
  27. Point(yAxis) → N
  28. Point(xAxis) → O
  29. Point(xAxis) → P
  30. Line(O, P) → j
  31. Point(yAxis) → Q
  32. Point(yAxis) → R
  33. Segment(Q, R) → i
  34. Textfield(n) → InputBox1
  35. Angle(C, F, C') → α
  36. Angle(N, A, D) → β
  37. Angle(G, A, N) → γ
  38. Ray(A, M) → k

AI Drawing Prompt Reference

Draw a diagram demonstrating total internal reflection, showing incident and reflected rays, normal line, angles of incidence and reflection, and critical angle. The light ray should enter from the left, reflect at the interface, illustrating the law of reflection and Snell's law. Include angle measurements, vector representations, and geometric transformations like rotations and reflections to clearly demonstrate the phenomenon and calculations.
The prompt above was compiled from the original drawing commands and is for reference only.