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Reflection in a Plane Mirror

Reflection in a Plane Mirror
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2016-09-04 17:41
AngleTransformationGeometric Construction
This applet demonstrates the law of reflection and image formation in a plane mirror. Key mathematical concepts include the reflection law and geometric transformations. Using GeoGebra commands such as Mirror, Segment, and Point, the applet constructs reflected rays and image positions. Suitable for middle school and above students to learn about geometric transformations and optics.

GeoGebra Commands & Parameters

  1. Mirror(A_1, yAxis) → B
  2. Segment(A_1, B) → a
  3. Point(a) → D
  4. OrthogonalLine(D, a) → b
  5. Segment(S, D) → c
  6. Point(b) → F
  7. Angle(F, D, S) → α
  8. Mirror(S, b) → Source
  9. Segment(D, Source) → d
  10. Point(b) → H
  11. Intersect(α, b, (-2.6127429465173326E-16, 1.0373688097266047)) → E
  12. Segment(F, H) → f
  13. Point(c) → G
  14. Point(c) → J
  15. Vector(G, J) → u
  16. Angle(Source, D, F) → β
  17. Angle(S, D, H) → γ
  18. Angle(H, D, Source) → δ
  19. Point(yAxis) → H1
  20. Vector(D, H1) → s
  21. Translate(A_1, s) → I1
  22. Translate(A_1, s) → A_1'
  23. Translate(B, s) → B'
  24. Segment(A_1', B') → t
  25. Translate(S, s) → J1
  26. Translate(F, s) → K1
  27. Translate(D, s) → D'
  28. Translate(Source, s) → S''_1
  29. Segment(D', S''_1) → a1
  30. Translate(S, s) → S'_1
  31. Translate(D, s) → D'_1
  32. Segment(S'_1, D'_1) → b1
  33. Point(b1) → L1
  34. Point(b1) → Q1
  35. Vector(L1, Q1) → u1
  36. Point(u1) → R1
  37. Mirror(J1, t) → J1'
  38. Segment(J1', H1) → g
  39. Point(t) → A
  40. Segment(J1, A) → h
  41. Segment(J1', A) → i
  42. Vector(J1', A) → v
  43. Translate(A, v) → A'
  44. Segment(A, A') → j
  45. Point(t) → C
  46. Segment(J1, C) → k
  47. Segment(J1', C) → l
  48. Vector(J1', C) → w
  49. Translate(C, w) → C'
  50. Segment(C, C') → m