Light Reflection on a Half Cylinder

GeoGebra Commands & Parameters

1. Circle(M, 3.6) → g
2. Circle(M, 6) → e
3. Point(e) → Lq
4. Circle(M, 3.65) → c_1
5. Point(c_1) → A
6. Mirror(A, M) → A_1
7. Segment(A, A_1) → a
8. OrthogonalLine(M, a) → lot
9. Intersect(g, lot) → E, F
10. Angle(Lq, M, E) → α
11. If(α < π / 2, true, false) → oben
12. Rotate(Bild1, Angle[B, M, A], M) → Bild1'
13. Point(a) → C
14. Mirror(C, M) → C_1
15. CircleSector(M, C_1, C) → d_1
16. Segment(Lq, M) → b
17. Intersect(g, b) → G,
18. OrthogonalLine(G, lot) → h
19. Intersect(h, lot) → H
20. Segment(H, G) → s_1
21. Line(G, H) → i
22. Circle(H, s_1 / n) → k
23. Intersect(k, i) → I, J
24. Line(J, lot) → j
25. Intersect(g, j) → K, L
26. Ray(M, L) → l
27. Intersect(e, l) → N,
28. Vector(M, L) → b_1
29. Ray(M, J) → m
30. Intersect(e, m) → O,
31. If(oben ≟ true, Max[π / 2 - Angle[A, M, Lq], Angle[A, M, Lq] - π / 2], Max[(3 * π / 2) - Angle[A, M, Lq], Angle[A, M, Lq] - (3 * π / 2)]) → wa
32. Angle(F, M, Lq) → α_u
33. Mirror(Lq, lot) → Lq'
34. Mirror(M, lot) → M'
35. Segment(Lq', M') → b'
36. Segment(G, M') → b_2
37. Mirror(G, lot) → G'
38. Mirror(M', lot) → M''
39. Segment(G', M'') → b_3
40. Segment(M', K) → b_4
41. Segment(M', G') → b_5
42. Vector(M', F) → u
43. Angle(u, b_1) → β_o
44. Angle(E, M, K) → β_u
45. Segment(M, L) → d
46. CircleArc(M, C_1, C) → f
47. Segment(C_1, C) → p
48. Max(π / 2 - Angle[L, M, A], Angle[L, M, A] - π / 2) → wb
49. Angle(b_4, b_5) → wb4b5
50. Polygon(H_1, H_2, H_3, H_4) → Vieleck1, d_2, p_1, q, r
51. Angle(Vector[L], Vector[M]) → β
52. Angle(L, M, G') → γ