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棱镜分散白光

棱镜分散白光
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2016-01-11 14:49
解析几何变换几何作图
这个范例演示了棱镜如何分散白光。核心数学概念包括光的折射和色散。通过使用GeoGebra命令如Point, Polygon, OrthogonalLine等，可以构造棱镜和光线路径。适合高中物理和数学教学。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Polygon(A, B, 3) → poly1, c, a, b, C
  3. Point(b) → D_2
  4. OrthogonalLine(D_2, b) → e
  5. Point(e) → F
  6. Point(e) → G
  7. Angle(F, D_2, E) → α
  8. Ray(D_2, E) → d
  9. Slope(d) → m
  10. Rotate(G, asin((n_1 / n_2 * sin(α))), D_2) → G'
  11. Ray(D_2, G') → f
  12. Intersect(a, f) → H
  13. Segment(H, D_2) → g
  14. OrthogonalLine(H, a) → h
  15. Point(h) → I
  16. Angle(D_2, H, I) → γ
  17. Point(h) → J
  18. Rotate(J, (-asin((n_2 / n_1 * sin(γ)))), H) → J'
  19. Angle(J', H, J) → δ
  20. Ray(H, J') → i
  21. Segment(F, G) → j
  22. Segment(J, I) → k
  23. Angle(G, D_2, G') → β
  24. Rotate(G, asin((n_1 / (((1 + (0.002 * D)) * n_2)) * sin(α))), D_2) → P
  25. Rotate(G, asin((n_1 / (((1 + (0.004 * D)) * n_2)) * sin(α))), D_2) → Q
  26. Rotate(G, asin((n_1 / (((1 + (0.006 * D)) * n_2)) * sin(α))), D_2) → R
  27. Rotate(G, asin((n_1 / (((1 + (0.008 * D)) * n_2)) * sin(α))), D_2) → S
  28. Ray(D_2, P) → s
  29. Ray(D_2, Q) → t
  30. Ray(D_2, R) → a_1
  31. Ray(D_2, S) → b_1
  32. Rotate(G, asin((n_1 / (((1 + (0.01 * D)) * n_2)) * sin(α))), D_2) → T
  33. Ray(D_2, T) → c_1
  34. Intersect(a, s) → U
  35. Intersect(a, a_1) → V
  36. Intersect(a, t) → W
  37. Intersect(a, b_1) → Z
  38. Intersect(a, c_1) → A_1
  39. OrthogonalLine(U, a) → d_1
  40. OrthogonalLine(W, a) → e_1
  41. OrthogonalLine(V, a) → f_1
  42. OrthogonalLine(Z, a) → i_1
  43. OrthogonalLine(A_1, a) → l_1
  44. Point(d_1) → B_1
  45. Point(e_1) → C_1
  46. Point(f_1) → D_1
  47. Point(i_1) → E_1
  48. Point(l_1) → F_1
  49. Rotate(B_1, (-asin((((1 + (0.002 * D)) * n_2 / n_1) * sin(γ)))), U) → G_1
  50. Rotate(C_1, (-asin((((1 + (0.004 * D)) * n_2 / n_1) * sin(γ)))), W) → H_1
  51. Rotate(D_1, (-asin((((1 + (0.006 * D)) * n_2 / n_1) * sin(γ)))), V) → I_1
  52. Rotate(E_1, (-asin((((1 + (0.008 * D)) * n_2 / n_1) * sin(γ)))), Z) → J_1
  53. Rotate(F_1, (-asin((((1 + (0.01 * D)) * n_2 / n_1) * sin(γ)))), A_1) → K_1
  54. Ray(U, G_1) → n
  55. Ray(W, H_1) → p
  56. Ray(V, I_1) → q
  57. Ray(Z, J_1) → r
  58. Ray(A_1, K_1) → l
  59. Segment(D_2, U) → g_1
  60. Segment(D_2, V) → h_1
  61. Segment(D_2, Z) → j_1
  62. Segment(D_2, A_1) → k_1
  63. Segment(D_2, W) → m_1
  64. Intersect(b, a) → K
  65. Intersect(b, c) → L
  66. Intersect(a, c) → M
  67. Polygon(K, L, M) → poly2, m_2, k_2, l_2