Multiple Prism Refractions - Lens Construction

GeoGebra Commands & Parameters

1. Polygon(A, B, C, D) → poly1, a, b, c, d
2. Point(d) → E
3. Ray(E, F) → f
4. OrthogonalLine(E, d) → g
5. Angle(g, f) → α
6. Point(g) → G
7. Rotate(G, asin((1 / n * sin(α))), E) → G'
8. Angle(G, E, G') → β
9. Ray(E, G') → h
10. Intersect(b, h) → H
11. Segment(E, H) → i
12. OrthogonalLine(H, b) → j
13. Point(j) → I
14. Angle(G', H, I) → γ
15. Point(j) → J
16. Rotate(J, (-asin((n * sin(γ)))), H) → J'
17. Angle(J', H, J) → δ
18. Ray(H, J') → k
19. Polygon(A_1, B_1, C_1, D_1) → poly1_1, a_1, b_1, c_1, d_1
20. Point(d_1) → E_1
21. Ray(E_1, F_1) → f_1
22. OrthogonalLine(E_1, d_1) → g_1
23. Angle(g_1, f_1) → α_1
24. Point(g_1) → G_1
25. Rotate(G_1, asin((1 / n * sin(α_1))), E_1) → G'_1
26. Angle(G_1, E_1, G'_1) → β_1
27. Ray(E_1, G'_1) → h_1
28. Intersect(b_1, h_1) → H_1
29. Segment(E_1, H_1) → i_1
30. OrthogonalLine(H_1, b_1) → j_1
31. Point(j_1) → I_1
32. Angle(G'_1, H_1, I_1) → γ_1
33. Point(j_1) → J_1
34. Rotate(J_1, (-asin((n * sin(γ_1)))), H_1) → J'_1
35. Angle(J'_1, H_1, J_1) → δ_1
36. Ray(H_1, J'_1) → k_1
37. Polygon(A_2, B_2, C_2, D_2) → poly1_2, a_2, b_2, c_2, d_2
38. Point(d_2) → E_2
39. Ray(E_2, F_2) → f_2
40. OrthogonalLine(E_2, d_2) → g_2
41. Angle(g_2, f_2) → α_2
42. Point(g_2) → G_2
43. Rotate(G_2, asin((1 / n * sin(α_2))), E_2) → G'_2
44. Angle(G_2, E_2, G'_2) → β_2
45. Ray(E_2, G'_2) → h_2
46. Intersect(b_2, h_2) → H_2
47. Segment(E_2, H_2) → i_2
48. OrthogonalLine(H_2, b_2) → j_2
49. Point(j_2) → I_2
50. Angle(G'_2, H_2, I_2) → γ_2
51. Point(j_2) → J_2
52. Rotate(J_2, (-asin((n * sin(γ_2)))), H_2) → J'_2
53. Angle(J'_2, H_2, J_2) → δ_2
54. Ray(H_2, J'_2) → k_2
55. Polygon(A_3, B_3, C_3, D_3) → poly1_3, a_3, b_3, c_3, d_3
56. Point(d_3) → E_3
57. Ray(E_3, F_3) → f_3
58. OrthogonalLine(E_3, d_3) → g_3
59. Angle(g_3, f_3) → α_3
60. Point(g_3) → G_3
61. Rotate(G_3, asin((1 / n * sin(α_3))), E_3) → G'_3
62. Angle(G_3, E_3, G'_3) → β_3
63. Ray(E_3, G'_3) → h_3
64. Intersect(b_3, h_3) → H_3
65. Segment(E_3, H_3) → i_3
66. OrthogonalLine(H_3, b_3) → j_3
67. Point(j_3) → I_3
68. Angle(G'_3, H_3, I_3) → γ_3
69. Point(j_3) → J_3
70. Rotate(J_3, (-asin((n_2 * sin(γ_3)))), H_3) → J'_3
71. Angle(J'_3, H_3, J_3) → δ_3
72. Ray(H_3, J'_3) → k_3
73. Polygon(A_4, B_4, C_4, D_4) → poly1_4, a_4, b_4, c_4, d_4
74. Point(d_4) → E_4
75. Ray(E_4, F_4) → f_4
76. OrthogonalLine(E_4, d_4) → g_4
77. Angle(g_4, f_4) → α_4
78. Point(g_4) → G_4
79. Rotate(G_4, asin((1 / n * sin(α_4))), E_4) → G'_4
80. Angle(G_4, E_4, G'_4) → β_4
81. Ray(E_4, G'_4) → h_4
82. Intersect(b_4, h_4) → H_4
83. Segment(E_4, H_4) → i_4
84. OrthogonalLine(H_4, b_4) → j_4
85. Point(j_4) → I_4
86. Angle(G'_4, H_4, I_4) → γ_4
87. Point(j_4) → J_4
88. Rotate(J_4, (-asin((n_3 * sin(γ_4)))), H_4) → J'_4
89. Angle(J'_4, H_4, J_4) → δ_4
90. Ray(H_4, J'_4) → k_4