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两面镜子的光线反射

两面镜子的光线反射
几何画板及绘图内容加载中，请稍等……
2014-06-23 23:23
角向量数列几何作图
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①本范例演示了单光源在两面镜子之间多次反射的光线路径；②涉及的核心数学概念包括反射定律、角度计算、向量运算和序列生成；③作图要点使用了GeoGebra命令：Circle, Vector, Point, UnitOrthogonalVector, UnitVector, Angle, Segment, If, Reflection2b, IndexOf, Ray, Sequence；④适合高中物理光学和数学几何教学，用于理解光的反射现象和几何序列构建。

GeoGebra 命令及参数

  1. Circle(B, 1) → q
  2. Vector(A, B) → g
  3. Point(q) → G
  4. Vector(B, G) → nrm2
  5. UnitOrthogonalVector(nrm2) → m2
  6. Circle(A, 1) → r_1
  7. Vector(X0, A) → f
  8. UnitVector(Vector[UnitVector[g] - UnitVector[f]]) → u
  9. Point(r_1) → F
  10. Vector(A, F) → nrm1
  11. UnitOrthogonalVector(nrm1) → m1
  12. Circle(X0, 1) → d_1
  13. Point(d_1) → T
  14. UnitVector(xAxis) → X
  15. UnitVector(yAxis) → Y
  16. UnitOrthogonalVector(u) → w
  17. Angle(nrm1, m1) → β
  18. Vector(X0, T) → r0
  19. Angle(nrm2, m2) → α
  20. Segment(A - m1, A + m1) → mirror1
  21. whichMirror2(X0, T, P1, Q1, P2, Q2) → t1
  22. Segment(B - m2, B + m2) → mirror2
  23. If(t1 ≟ 2, B, A) → Z1
  24. If(t1 ≟ 2, m2, m1) → x1
  25. If(t1 ≟ 2, A, B) → Z2
  26. If(t1 ≟ 2, m1, m2) → x2
  27. If(t1 ≟ 2, nrm2, nrm1) → n1
  28. If(t1 ≟ 2, nrm1, nrm2) → n2
  29. Reflection2b(X0, T, Z1 + x1, Z1 - x1, n1, true) → r1, X1, beam1
  30. Reflection2b(X1, X1 + r1, Z2 + x2, Z2 - x2, n2, true) → r2, X2, beam2
  31. Reflection2b(X2, X2 + r2, Z1 + x1, Z1 - x1, n1, true) → r3, X3, beam3
  32. Reflection2b(X3, X3 + r3, Z2 + x2, Z2 - x2, n2, true) → r4, X4, beam4
  33. Reflection2b(X4, X4 + r4, Z1 + x1, Z1 - x1, n1, true) → r5, X5, beam5
  34. Reflection2b(X5, X5 + r5, Z2 + x2, Z2 - x2, n2, true) → r6, X6, beam6
  35. Reflection2b(X6, X6 + r6, Z1 + x1, Z1 - x1, n1, true) → r7, X7, beam7
  36. Reflection2b(X7, X7 + r7, Z2 + x2, Z2 - x2, n2, true) → r8, X8, beam8
  37. Reflection2b(X8, X8 + r8, Z1 + x1, Z1 - x1, n1, true) → r9, X9, beam9
  38. Reflection2b(X9, X9 + r9, Z2 + x2, Z2 - x2, n2, true) → r10, X10, beam10
  39. Reflection2b(X10, X10 + r10, Z1 + x1, Z1 - x1, n1, true) → r11, X11, beam11
  40. Reflection2b(X11, X11 + r11, Z2 + x2, Z2 - x2, n2, true) → r12, X12, beam12
  41. Reflection2b(X12, X12 + r12, Z1 + x1, Z1 - x1, n1, true) → r13, X13, beam13
  42. Reflection2b(X13, X13 + r13, Z2 + x2, Z2 - x2, n2, true) → r14, X14, beam14
  43. Reflection2b(X14, X14 + r14, Z1 + x1, Z1 - x1, n1, true) → r15, X15, beam15
  44. Reflection2b(X15, X15 + r15, Z2 + x2, Z2 - x2, n2, true) → r16, X16, beam16
  45. Reflection2b(X16, X16 + r16, Z1 + x1, Z1 - x1, n1, true) → r17, X17, beam17
  46. IndexOf(0, Zip[abs(k), k, list1]) → d
  47. If(Defined[d], d, 18) → i
  48. whichMirror2(X17, X17 + r17, P1, Q1, P2, Q2) → k
  49. Ray(Object["X" + (i - 1)], Vector[Object["r" + (i - 1)]]) → a
  50. Sequence(4 - round(k / 5), k, 0, 17) → list3

AI 绘图提示语参考

绘制一个单光线在两个平行镜面之间多次反射的路径。首先画两个圆表示镜面，然后画出光线的初始方向和入射点。接着，根据反射定律，依次计算每次反射后的光线方向和路径，直到光线路径变得不明显为止。
以上提示语为根据原始绘图命令整理而来，仅供参考。