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Reflection on Convex Mirror: Spherical Surface

Reflection on Convex Mirror: Spherical Surface
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2015-02-06 00:37
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the reflection of a linear object on a convex mirror. Key mathematical concepts include spherical geometry and the law of reflection. Using GeoGebra commands such as Point, Semicircle, Line, and Intersect, the trajectory of the reflected light can be constructed. Suitable for high school physics and mathematics education.

GeoGebra Commands & Parameters

  1. Point(xAxis) → C
  2. Point(yAxis) → B
  3. Semicircle(B, C_1) → MirrorConvex
  4. Point(xAxis) → F
  5. Point(xAxis) → Directriz
  6. Line(Directriz, yAxis) → a
  7. Point(xAxis) → P
  8. Intersect(MirrorConvex, xAxis, 1) → O
  9. Parabola(F, a) → k
  10. Line(P, yAxis) → b
  11. Point(b) → P_1
  12. Vector(P, P_1) → u
  13. Line(P_1, xAxis) → c
  14. Intersect(MirrorConvex, c, 1) → A
  15. Vector(P_1, A) → v
  16. Tangent(A, MirrorConvex) → d,
  17. OrthogonalLine(A, d) → e
  18. Angle(c, e) → θ_i
  19. Point(e) → G
  20. Rotate(G, θ_i, A) → G'
  21. Angle(G, A, G') → θ_ir
  22. Line(A, G') → f
  23. Vector(A, G') → w
  24. Line(P_1, F) → g
  25. Intersect(MirrorConvex, g, 1) → E
  26. Vector(P_1, E) → h
  27. Line(E, xAxis) → i
  28. Point(i) → H
  29. Vector(E, H) → j
  30. Line(P_1, C) → l
  31. Intersect(MirrorConvex, l, 1) → I
  32. Vector(P_1, I) → m
  33. Point(l) → J
  34. Vector(I, J) → n
  35. Intersect(f, i) → K
  36. Line(K, u) → p
  37. Intersect(p, xAxis) → L
  38. Vector(L, K) → q
  39. Vector(L, K) → r