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平行表面折射 by Barb Newitt

平行表面折射 by Barb Newitt
几何画板及绘图内容加载中，请稍等……
2016-09-14 11:25
角向量几何作图函数图像
①本范例演示光线在平行表面间的折射现象；②涉及核心数学概念包括折射定律、角度计算、向量运算；③构造过程中运用了Point, Line, Intersect, OrthogonalLine, Segment, Angle, Rotate, Vector, Circle, AngularBisector, Mirror, Ray, Distance, Midpoint等GeoGebra命令与对象；④适合高中物理与数学教学，用于理解折射原理与几何作图。

GeoGebra 命令及参数

  1. Point(yAxis) → F
  2. Point(yAxis) → E
  3. Line(E, F) → g
  4. Intersect(xAxis, yAxis) → D
  5. OrthogonalLine(D, g) → h
  6. Point(h) → K
  7. Segment(A, B) → f
  8. Intersect(h, f) → G
  9. Point(f) → C
  10. Angle(G, D, C) → β
  11. Angle(C, D, G) → α
  12. If(α > 90°, β, α) → γ
  13. Rotate(K, a, D) → K'
  14. Line(D, K') → g_1
  15. Polygon(R, S, T, U) → poly2, r, s, t_1, u_1
  16. Intersect(g_1, t_1) → V
  17. Vector(C, D) → u
  18. Circle(D, 1.2) → c
  19. AngularBisector(C, D, G) → i
  20. Intersect(c, i, 2) → H
  21. Mirror(C, h) → C'
  22. Vector(D, C') → v
  23. AngularBisector(C', D, G) → j
  24. Intersect(c, j, 2) → I
  25. Angle(C', D, G) → δ
  26. Angle(G, D, C') → ε
  27. If(δ > 90°, ε, δ) → ζ
  28. Circle(D, 1.8) → d
  29. Intersect(d, j, 2) → J
  30. Angle(K, D, K') → η
  31. Rotate(K, (-a), D) → K'_1
  32. Angle(K'_1, D, K) → θ
  33. AngularBisector(K'_1, D, K) → k
  34. AngularBisector(K, D, K') → l
  35. Intersect(c, k, 2) → L
  36. Intersect(c, l, 2) → M
  37. Vector(D, K'_1) → w
  38. Vector(D, K') → b
  39. Polygon(N, O, P, Q) → poly1, n, o, p, q
  40. Textfield(n_1) → InputBox1
  41. Textfield(n_2) → InputBox2
  42. Line(C, D) → m
  43. OrthogonalLine(C, m) → f_1
  44. Circle(C, 0.6) → e
  45. Intersect(e, f_1, 2) → Z
  46. Intersect(e, f_1, 1) → A_1
  47. Line(D, K'_1) → h_1
  48. Intersect(h_1, t_1) → W
  49. Vector(D, V) → v_1
  50. Vector(D, W) → w_1
  51. Rotate(B_1, (-γ), W) → C_1
  52. Angle(C_1, W, B_1) → ν
  53. Point(h) → D_1
  54. Point(h) → E_1
  55. Segment(D_1, E_1) → i_1
  56. Vector(W, C_1) → a_1
  57. Rotate(G_1, γ, V) → F_1
  58. Angle(G_1, V, F_1) → ξ
  59. Vector(V, F_1) → b_1
  60. Ray(C, D) → j_1
  61. Segment(H_1, I_1) → k_1
  62. Segment(J_1, K_1) → l_1
  63. AngularBisector(F_1, V, G_1) → m_1
  64. AngularBisector(B_1, W, C_1) → p_1
  65. Circle(W, 1) → c_1
  66. Circle(V, 1) → d_1
  67. Intersect(d_1, m_1, 2) → L_1
  68. Intersect(c_1, p_1, 2) → M_1
  69. Angle(D, W, J_1) → ο
  70. Angle(H_1, V, D) → ρ
  71. AngularBisector(J_1, W, D) → q_1
  72. AngularBisector(D, V, H_1) → r_1
  73. Intersect(d_1, r_1, 2) → N_1
  74. Intersect(c_1, q_1, 2) → O_1
  75. Intersect(t_1, j_1) → P_1
  76. OrthogonalLine(P_1, j_1) → s_1
  77. Line(W, C_1) → e_1
  78. Intersect(s_1, e_1) → Q_1
  79. Distance(P_1, Q_1) → distanceP1Q1
  80. Textfield(t) → InputBox3
  81. Midpoint(P_1, Q_1) → R_1
  82. Vector(P_1, Q_1) → u_2
  83. Vector(Q_1, P_1) → v_2
  84. Line(F_1, V) → f_2
  85. Intersect(f_2, s_1) → S_1
  86. Midpoint(P_1, S_1) → T_1
  87. Vector(S_1, P_1) → w_2
  88. Vector(P_1, S_1) → a_2
  89. Distance(P_1, S_1) → o_1
  90. Distance(P_1, S_1) → b_2
  91. Point(r) → U_1
  92. Point(t_1) → V_1
  93. Vector(U_1, V_1) → c_2
  94. Vector(V_1, U_1) → d_2