棱镜中的全内反射（角反射器）

GeoGebra 命令及参数

1. Line(A, C) → m_1
2. Polygon(A, B, C) → poly1, c, a, b
3. Point(b) → D
4. OrthogonalLine(D, b) → f
5. Circle(D, 2) → e
6. Intersect(e, m_1, 1) → Z
7. Intersect(e, m_1, 2) → W
8. Semicircle(W, Z) → p_1
9. Point(p_1) → G
10. Circle(D, 0.5) → d
11. Intersect(d, f, 2) → E
12. Intersect(d, f, 1) → F
13. Segment(E, F) → g
14. Angle(E, D, G) → α
15. Rotate(F, asin(sin(α) / n), D) → F'
16. Angle(F, D, F') → β
17. Line(D, F') → i_3
18. Intersect(i_3, c) → H
19. Intersect(i_3, a) → I
20. Segment(J, K) → j
21. Angle(D, H, K) → γ
22. If(γ > asin(1 / n), Rotate[K, γ, H]) → K'
23. Angle(K, H, K') → δ
24. Rotate(J, -asin(n * sin(γ)), H) → J'
25. Angle(J', H, J) → ε
26. Line(H, K') → k
27. Intersect(k, a) → L
28. Segment(D, H) → l
29. Segment(H, L) → m
30. Segment(M, N) → p
31. Angle(H, L, M) → ζ
32. If(ζ > asin(1 / n), Rotate[M, ζ, L]) → M'
33. Angle(M, L, M') → η
34. Rotate(N, -asin(n * sin(ζ)), L) → N'
35. Angle(N', L, N) → θ
36. Line(L, M') → q
37. Intersect(q, b) → O
38. Segment(L, O) → r_3
39. Circle(O, 0.5) → s
40. OrthogonalLine(O, b) → t
41. Intersect(s, t, 2) → P
42. Intersect(s, t, 1) → Q
43. Segment(P, Q) → a_1
44. Angle(L, O, Q) → ι
45. Rotate(P, -asin(n * sin(ι)), O) → P'
46. Angle(P', O, P) → κ
47. Circle(O, 2) → c_1
48. Line(O, P') → b_1
49. Intersect(c_1, b_1, 2) → R
50. Segment(O, R) → d_1
51. Circle(H, 1.5) → e_1
52. Line(H, J') → f_1
53. Intersect(e_1, f_1, 2) → S
54. Segment(H, S) → g_1
55. Circle(L, 1.5) → h_1
56. Line(L, N') → i_1
57. Intersect(h_1, i_1, 2) → T
58. Segment(L, T) → j_1
59. Segment(D, I) → k_1
60. Segment(U, V) → l_1
61. Segment(G, D) → h
62. Angle(U, I, D) → λ
63. If(λ > asin(1 / n), Rotate[U, -λ, I]) → U'
64. Angle(U', I, U) → μ
65. Rotate(V, asin(n * sin(λ)), I) → V'
66. Angle(V, I, V') → ν
67. Circle(I, 1.5) → q_1
68. Line(I, V') → n_1
69. Intersect(q_1, n_1, 2) → A_1
70. Segment(I, A_1) → r_1
71. Line(I, U') → s_1
72. Intersect(s_1, c) → B_1
73. Segment(I, B_1) → t_1
74. Segment(C_1, D_1) → a_2
75. Circle(B_1, 1.5) → c_2
76. Angle(D_1, B_1, I) → ξ
77. If(ξ > asin(1 / n), Rotate[D_1, -ξ, B_1]) → E_1
78. Angle(E_1, B_1, D_1) → ο
79. Line(B_1, E_1) → b_2
80. Intersect(m_1, b_2) → F_1
81. Segment(B_1, F_1) → d_2
82. Rotate(C_1, asin(n * sin(ξ)), B_1) → G_1
83. Angle(C_1, B_1, G_1) → ρ
84. Line(B_1, G_1) → e_2
85. Intersect(c_2, e_2, 2) → H_1
86. Segment(B_1, H_1) → f_2
87. Circle(F_1, 0.5) → g_2
88. Circle(F_1, 2) → h_2
89. OrthogonalLine(F_1, b) → i_2
90. Intersect(g_2, i_2, 1) → I_1
91. Intersect(g_2, i_2, 2) → J_1
92. Segment(I_1, J_1) → j_2
93. Angle(I_1, F_1, B_1) → σ
94. Rotate(J_1, asin(n * sin(σ)), F_1) → K_1
95. Angle(J_1, F_1, K_1) → τ
96. Line(F_1, K_1) → k_2
97. Intersect(h_2, k_2, 2) → L_1
98. Segment(F_1, L_1) → l_2
99. Angle(A, B, C) → υ
100. Angle(B, C, A) → χ
101. Angle(C, A, B) → ϕ
102. Line(H, K') → m_2
103. Line(I, U') → p_2
104. Line(I, U') → q_2
105. Intersect(q_2, b) → P_1
106. Line(P_1, I) → r_2
107. Intersect(q_1, r_2) → Q_1, R_1
108. Point(r_2) → S_1
109. Segment(S_1, Q_1) → s_2
110. Intersect(b, m_2) → M_1
111. Line(H, M_1) → n_2
112. Intersect(e_1, n_2) → N_1, O_1
113. Segment(H, O_1) → t_2
114. Angle(E, D, G) → i
115. Angle(P, O, R) → r