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Reflection from a Curved Mirror

Reflection from a Curved Mirror
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2014-11-05 11:29
CircleGeometric ConstructionSlider Animation
This example demonstrates the reflection of parallel light rays from a concave mirror, involving reflection laws, geometric construction, and circular arcs. The construction uses GeoGebra commands like CircleArc, Segment, and Angle to create the mirror surface and adjust the radius. It is suitable for middle or high school mathematics to understand the connection between optics and geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. CircleArc(MC, Mt, Mb) → Mirror
  3. Intersect(Mirror, l1, 1) → Mp1
  4. Intersect(Mirror, l2, 1) → Mp2
  5. Segment(Mp1, MC) → r1
  6. Segment(Mp2, MC) → r2
  7. Angle(l1, r1) → α1
  8. Angle(l2, r2) → α2
  9. Point(r1) → R1p
  10. Point(r2) → R2p
  11. Rotate(R1p, (-α1), Mp1) → R1p'
  12. Ray(Mp1, R1p') → ryRt_1
  13. Rotate(R2p, (-α2), Mp2) → R2p'
  14. Ray(Mp2, R2p') → ryRt_2
  15. Intersect(Mirror, l3, 1) → Mp3
  16. Intersect(Mirror, l4, 1) → Mp4
  17. Intersect(Mirror, l5, 1) → Mp5
  18. Segment(Mp3, MC) → r3
  19. Segment(Mp4, MC) → r4
  20. Segment(Mp5, MC) → r5
  21. Point(r3) → R3p
  22. Point(r4) → R4p
  23. Point(r5) → R5p
  24. Angle(l3, r3) → α3
  25. Angle(l4, r4) → α4
  26. Angle(l5, r5) → α5
  27. Rotate(R3p, (-α3), Mp3) → R3p'
  28. Rotate(R4p, (-α4), Mp4) → R4p'
  29. Ray(Mp3, R3p') → ryRt_3
  30. Ray(Mp4, R4p') → ryRt_4
  31. Rotate(R5p, (-α5), Mp5) → R5p'
  32. Ray(Mp5, R5p') → ryRt_5
  33. Intersect(Mirror, j5, 1) → Mq5
  34. Intersect(Mirror, j4, 1) → Mq4
  35. Intersect(Mirror, j3, 1) → Mq3
  36. Intersect(Mirror, j2, 1) → Mq2
  37. Intersect(Mirror, j1, 1) → Mq1
  38. Segment(Mq5, MC) → r5b
  39. Segment(Mq4, MC) → r4b
  40. Segment(Mq3, MC) → r3b
  41. Segment(Mq2, MC) → r2b
  42. Segment(Mq1, MC) → r1b
  43. Point(r5b) → R5pb
  44. Point(r4b) → R4pb
  45. Point(r3b) → R3pb
  46. Point(r2b) → R2pb
  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

AI Drawing Prompt Reference

Draw a reflection diagram of a concave mirror. The mirror is a circular arc centered at the origin. Parallel light rays from the left reflect off the mirror and converge at the focal point. Two light paths are shown to illustrate the reflection law. Intersection points on the mirror are marked as key points. The overall diagram combines optics and geometry, suitable for math education.
The prompt above was compiled from the original drawing commands and is for reference only.