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Snell's Law Demonstration by Ryan Hirst

Snell's Law Demonstration by Ryan Hirst
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2013-02-14 09:01
AngleVectorGeometric ConstructionSlider Animation
In collections Light
This example demonstrates the refraction of light passing through different media. Key mathematical concepts include Snell's Law, angle of incidence, angle of refraction, and index of refraction. Construction involves Geogebra commands such as Intersect, Circle, Point, Vector, Line, UnitOrthogonalVector, Translate, Ray, Segment, and CircleArc to model the phenomenon. Suitable for high school physics and mathematics education to understand the principles of light refraction and calculations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, 1) → c
  3. Point(c) → l
  4. Point(c, 0.5) → u
  5. Vector(O, u) → U
  6. Line(l', U) → p_1
  7. UnitOrthogonalVector(U) → N
  8. Vector(O, l) → L
  9. Point(O, T) → t
  10. Line(O, u) → f_1
  11. Line(t, N) → m_1
  12. Translate(O, Vector[SideL * u, M']) → O'
  13. Point(O, N) → n_2
  14. If(rotSin > 0, 1, -1) → σ
  15. Ray(O, l') → d
  16. Ray(O, t) → e
  17. Segment(t, -(T * (-N)) * n_2) → h
  18. Line(O', M') → q
  19. Intersect(q, d) → L'
  20. Intersect(q, e) → t'
  21. CircleArc(O, B, u) → r_1
  22. Segment(u, B) → a_1
  23. Line(L', N) → b_1
  24. If(abs(rotCos) > 0.001, true, false) → w
  25. Segment(O', M') → g_1
  26. Segment(M', L') → h_1
  27. Segment(t, Intersect[m_1, f_1]) → tx
  28. Segment(l', Intersect[p_1, Line[O, N]]) → k_1
  29. Intersect(k_1, tx) → E
  30. Segment(O, L') → j
  31. Segment(O, O') → p
  32. Angle(T, Vector[-UpL * N]) → θ_2
  33. Angle(L, Vector[UpL * N]) → θ_1
  34. Ray(O, R) → i
  35. Segment(l, L * N * n_2) → g
  36. Ray(O, l) → b
  37. Point(b) → A
  38. Point(O, Vector[2 * T]) → C
  39. Segment(A, l) → s
  40. Segment(t, C) → j_1
  41. Point(O, Vector[2 * R]) → D
  42. Segment(r, D) → l_1
  43. Intersect(c, r_1, 1) → G
  44. Intersect(c, r_1, 1) → I
  45. Intersect(c, r_1) → J, , ,
  46. If(UpL ≟ 1, true, false) → Top
  47. Angle(Vector[-N], R) → α
  48. Segment(SideL * u, M') → f
  49. Ray(O, E) → n
  50. Line(l', N) → c_1
  51. Intersect(b_1, f_1) → IOR
  52. Distance(O, I) → OI
  53. If(z > 0, If[N * L > 0, η_2 / η_1, η_1 / η_2], "Total Internal Refraction") → n_1
  54. Intersect(m_1, p_1) → F
  55. Segment(F, t) → q_1
  56. Segment(l', F) → s_1
  57. Ray(O, F) → t_1

AI Drawing Prompt Reference

Draw a diagram demonstrating the refraction of light, including a circle and two lines, one tangent to the circle and the other intersecting the circle at the origin, showing the angle of incidence and refraction, with vectors indicating the direction of light and the normal direction, labeling the index of refraction and angle values, using a slider to adjust the angle of incidence and refraction to show the changes in refraction.
The prompt above was compiled from the original drawing commands and is for reference only.