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Geogebra Demonstration of Reflection & Refraction by Huygens Principle

Geogebra Demonstration of Reflection & Refraction by Huygens Principle
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2016-01-11 15:33
AngleVectorGeometric Construction
This example dynamically demonstrates the principles of light reflection and refraction using GeoGebra. It involves core mathematical concepts such as the law of reflection, Snell's law, angle measurement, and vector operations. Key GeoGebra commands used include Intersect, Line, OrthogonalLine, Point, Angle, Ray, Rotate, and Circle. Suitable for high school physics and mathematics education to help students visually understand optical principles.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → B
  2. Line(A_3, B) → a
  3. OrthogonalLine(B, xAxis) → b
  4. Point(b) → C
  5. Angle(C, B, A_3) → α
  6. OrthogonalLine(D, a) → c
  7. Corner(1) → E
  8. OrthogonalLine(E, xAxis) → d
  9. Intersect(c, d) → F
  10. Intersect(xAxis, c) → G
  11. Ray(B, A_3) → f
  12. OrthogonalLine(G, f) → g
  13. OrthogonalLine(G, f) → h
  14. Point(h) → I
  15. Ray(G, I) → i
  16. Point(xAxis) → A
  17. Rotate(U, (45° * β_1), B) → U'
  18. Point(i) → K
  19. Point(xAxis) → J
  20. Point(xAxis) → O
  21. Point(xAxis) → P_3
  22. Rotate(U, β_1, B) → U'_1
  23. Angle(U, B, U'_1) → β
  24. Ray(B, U'_1) → j
  25. Line(G, j) → e
  26. OrthogonalLine(G, e) → k
  27. Point(k) → L
  28. Ray(G, L) → l
  29. Rotate(M, π / 2 - α, B) → M'
  30. Angle(M, B, M') → δ
  31. Line(B, M') → p
  32. OrthogonalLine(G, p) → q
  33. Point(q) → N
  34. Ray(G, N) → r
  35. OrthogonalLine(A, l) → s
  36. Intersect(s, l) → Q
  37. Circle(A, Q) → c_1
  38. Intersect(c_1, xAxis) → R, S
  39. CircleArc(A, R, S) → d_1
  40. OrthogonalLine(A, r) → a_1
  41. Intersect(r, a_1) → T
  42. Circle(A, T) → e_1
  43. Intersect(e_1, xAxis) → V, W
  44. CircleArc(A, W, V) → f_1
  45. Ray(B, M') → b_1
  46. OrthogonalLine(O, l) → g_1
  47. Intersect(g_1, l) → A_1
  48. Circle(O, A_1) → h_1
  49. Intersect(h_1, xAxis) → B_1, C_1
  50. CircleArc(O, B_1, C_1) → k_1
  51. OrthogonalLine(P_3, l) → i_1
  52. Intersect(l, i_1) → D_1
  53. Circle(P_3, D_1) → p_1
  54. Intersect(p_1, xAxis) → E_1, F_1
  55. CircleArc(P_3, E_1, F_1) → q_1
  56. Point(xAxis) → G_1
  57. OrthogonalLine(G_1, l) → j_1
  58. Intersect(j_1, l) → H_1
  59. Circle(G_1, H_1) → r_1
  60. Intersect(r_1, xAxis) → I_1, J_1
  61. CircleArc(G_1, I_1, J_1) → s_1
  62. Point(xAxis) → K_1
  63. OrthogonalLine(K_1, l) → l_1
  64. Intersect(l, l_1) → L_1
  65. Circle(K_1, L_1) → t_1
  66. Intersect(t_1, xAxis) → M_1, N_1
  67. CircleArc(K_1, M_1, N_1) → c_2
  68. Intersect(j, l) → O_1
  69. Circle(B, O_1) → d_2
  70. Intersect(d_2, xAxis) → P_1, Q_1
  71. CircleArc(B, P_1, Q_1) → e_2
  72. Point(xAxis) → R_1
  73. OrthogonalLine(R_1, l) → m_1
  74. Intersect(m_1, l) → S_1
  75. Circle(R_1, S_1) → f_2
  76. Intersect(f_2, xAxis) → T_1, U_1
  77. CircleArc(R_1, T_1, U_1) → g_2
  78. Point(xAxis) → V_1
  79. OrthogonalLine(V_1, l) → n_1
  80. Intersect(l, n_1) → W_1
  81. Circle(V_1, W_1) → h_2
  82. Point(xAxis) → B_2
  83. OrthogonalLine(B_2, l) → a_2
  84. Intersect(l, a_2) → C_2
  85. Circle(B_2, C_2) → p_2
  86. Intersect(p_2, xAxis) → D_2, E_2
  87. CircleArc(B_2, D_2, E_2) → q_2
  88. OrthogonalLine(O, r) → b_2
  89. Intersect(r, b_2) → F_2
  90. Circle(O, F_2) → r_2
  91. Intersect(r_2, xAxis) → G_2, H_2
  92. CircleArc(O, H_2, G_2) → s_2
  93. OrthogonalLine(P_3, r) → i_2
  94. Intersect(r, i_2) → I_2
  95. Circle(P_3, I_2) → t_2
  96. Intersect(t_2, xAxis) → J_2, K_2
  97. CircleArc(P_3, K_2, J_2) → c_3
  98. OrthogonalLine(G_1, r) → j_2
  99. Intersect(j_2, r) → L_2
  100. Circle(G_1, L_2) → d_3
  101. Intersect(d_3, xAxis) → M_2, N_2
  102. CircleArc(G_1, N_2, M_2) → e_3
  103. Intersect(b_1, r) → O_2
  104. Circle(B, O_2) → f_3
  105. Intersect(f_3, xAxis) → P_2, Q_2
  106. CircleArc(B, Q_2, P_2) → g_3
  107. OrthogonalLine(K_1, r) → l_2
  108. Intersect(l_2, r) → R_2
  109. Circle(K_1, R_2) → h_3
  110. Intersect(h_3, xAxis) → S_2, T_2
  111. CircleArc(K_1, T_2, S_2) → k_3
  112. OrthogonalLine(R_1, r) → m_2
  113. Intersect(m_2, r) → U_2
  114. Circle(R_1, U_2) → p_3
  115. Intersect(p_3, xAxis) → V_2, W_2
  116. CircleArc(R_1, W_2, V_2) → q_3
  117. OrthogonalLine(V_1, r) → n_3
  118. Point(j) → C_3
  119. Point(xAxis) → E_3
  120. Polygon(I_3, G_3, H_3, F_3) → polígono1, i_3, g_4, h_4, f_4
  121. OrthogonalLine(A_3, b) → b_3
  122. Intersect(b_3, b_1) → D_3
  123. Intersect(c, i) → N_3
  124. Line(Corner[4], Corner[3]) → k_2
  125. Intersect(i, k_2) → Z_1
  126. Corner(4) → Z_2
  127. Intersect(f_1, r, 1) → H
  128. Vector(A, H) → v_1t
  129. Intersect(d_1, l, 1) → P
  130. Vector(A, P) → u

AI Drawing Prompt Reference

Draw a diagram illustrating light reflection and refraction. Start by drawing the intersection point B of the x-axis and y-axis. Then, draw a line a from point A_3 to B. Draw a perpendicular line b from B to the x-axis and take point C on b. Measure the angle α between points C, B, and A_3. Draw a perpendicular line c from B to line a and take point D on c. Draw a corner point E on the x-axis and a perpendicular line d from E to the x-axis, intersecting c at point F. Draw a ray f from B to A_3 and a perpendicular line g from G to f, intersecting d at point G. Draw a perpendicular line h from G to f and take point I. Draw a ray i from G to I. Draw a point A on the x-axis and rotate point U 45° * β_1 around B to get U'. Draw a ray j from B to U' and intersect it with f at point H. Draw a line e from G to H and intersect it with f at point K. Draw a perpendicular line l from G to e and take point M. Draw a ray m from B to M and intersect it with f at point N. Draw a line n from A to N and intersect it with f at point P. Draw a circle c_1 centered at A passing through P and intersecting the x-axis at points R and S. Draw an arc d_1 from A to R and S. Draw a perpendicular line s from A to l and intersect it with l at point Q. Draw a circle c_2 centered at A passing through Q and intersecting the x-axis at points V and W. Draw an arc f_1 from A to V and W. Draw a ray b_1 from B to M' and intersect it with f at point O. Draw a perpendicular line g_1 from O to l and intersect it with l at point P_1. Draw a circle h_1 centered at O passing through P_1 and intersecting the x-axis at points R_1 and S_1. Draw an arc j_1 from O to R_1 and S_1.
The prompt above was compiled from the original drawing commands and is for reference only.