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抛物面镜反射

抛物面镜反射
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2014-11-26 12:05
函数变换几何作图
该范例展示了平行于轴的入射光线在抛物面镜上的反射情况。核心数学概念包括反射定律和抛物线的性质。通过使用GeoGebra命令如Parabola, Intersect, Ray, Angle, Point, Rotate, Segment等，可以构造出抛物面镜反射的动态模型。适合高中物理和数学教学，帮助学生理解反射现象和抛物线的几何特性。

GeoGebra 命令及参数

  1. Parabola(F, dir) → Mirror
  2. Intersect(Mirror, j5, 1) → Mq5
  3. Intersect(Mirror, l5, 1) → Mp5
  4. Intersect(Mirror, j4, 1) → Mq4
  5. Intersect(Mirror, l4, 1) → Mp4
  6. Intersect(Mirror, j2, 1) → Mq2
  7. Intersect(Mirror, l2, 1) → Mp2
  8. Intersect(Mirror, j3, 1) → Mq3
  9. Intersect(Mirror, l3, 1) → Mp3
  10. Intersect(Mirror, j1, 1) → Mq1
  11. Intersect(Mirror, l1, 1) → Mp1
  12. Intersect(xAxis, yAxis) → O
  13. Ray(Mp1, cmp1) → r1
  14. Angle(l1, r1) → α1
  15. Ray(Mp2, cmp2) → r2
  16. Angle(l2, r2) → α2
  17. Point(r1) → R1p
  18. Point(r2) → R2p
  19. Rotate(R1p, (-α1), Mp1) → R1p'
  20. Ray(Mp1, R1p') → ryRt_1
  21. Rotate(R2p, (-α2), Mp2) → R2p'
  22. Ray(Mp2, R2p') → ryRt_2
  23. Ray(Mp3, cmp3) → r3
  24. Point(r3) → R3p
  25. Ray(Mp4, cmp4) → r4
  26. Point(r4) → R4p
  27. Ray(Mp5, cmp5) → r5
  28. Point(r5) → R5p
  29. Angle(l3, r3) → α3
  30. Angle(l4, r4) → α4
  31. Angle(l5, r5) → α5
  32. Rotate(R3p, (-α3), Mp3) → R3p'
  33. Rotate(R4p, (-α4), Mp4) → R4p'
  34. Ray(Mp3, R3p') → ryRt_3
  35. Ray(Mp4, R4p') → ryRt_4
  36. Rotate(R5p, (-α5), Mp5) → R5p'
  37. Ray(Mp5, R5p') → ryRt_5
  38. Ray(Mq5, cmp5b) → r5b
  39. Point(r5b) → R5pb
  40. Ray(Mq4, cmp4b) → r4b
  41. Point(r4b) → R4pb
  42. Ray(Mq3, cmp3b) → r3b
  43. Point(r3b) → R3pb
  44. Ray(Mq2, cmp2b) → r2b
  45. Point(r2b) → R2pb
  46. Ray(Mq1, cmp1b) → r1b
  47. Point(r1b) → R1pb
  48. Rotate(R1pb, α1, Mq1) → R1pb'
  49. Ray(Mq1, R1pb') → ryRb_1
  50. Rotate(R2pb, α2, Mq2) → R2pb'
  51. Ray(Mq2, R2pb') → ryRb_2
  52. Rotate(R3pb, α3, Mq3) → R3pb'
  53. Ray(Mq3, R3pb') → ryRb_3
  54. Rotate(R4pb, α4, Mq4) → R4pb'
  55. Ray(Mq4, R4pb') → ryRb_4
  56. Rotate(R5pb, α5, Mq5) → R5pb'
  57. Ray(Mq5, R5pb') → ryRb_5
  58. Point(l1) → Dt1
  59. Point(l2) → Dt2
  60. Point(l3) → Dt3
  61. Point(l4) → Dt4
  62. Point(l5) → Dt5
  63. Point(j5) → Db5
  64. Point(j4) → Db4
  65. Point(j3) → Db3
  66. Point(j2) → Db2
  67. Point(j1) → Db1
  68. Segment(Dt1, Mp1) → ryIt_1
  69. Segment(Dt2, Mp2) → ryIt_2
  70. Segment(Dt3, Mp3) → ryIt_3
  71. Segment(Dt4, Mp4) → ryIt_4
  72. Segment(Dt5, Mp5) → ryIt_5
  73. Segment(Db1, Mq1) → ryIb_1
  74. Segment(Db2, Mq2) → ryIb_2
  75. Segment(Db3, Mq3) → ryIb_3
  76. Segment(Db4, Mq4) → ryIb_4
  77. Segment(Db5, Mq5) → ryIb_5
  78. Parabola(F, dir) → g