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Dispersion of White Light by Prism

Dispersion of White Light by Prism
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2016-01-11 14:49
Coordinate GeometryTransformationGeometric Construction
This example demonstrates how a prism disperses white light. Key mathematical concepts include refraction and dispersion. Using GeoGebra commands such as Point, Polygon, OrthogonalLine, etc., the path of light through the prism is constructed. Suitable for high school physics and mathematics education.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Polygon(A, B, 3) → poly1, c, a, b, C
  3. Point(b) → D_2
  4. OrthogonalLine(D_2, b) → e
  5. Point(e) → F
  6. Point(e) → G
  7. Angle(F, D_2, E) → α
  8. Ray(D_2, E) → d
  9. Slope(d) → m
  10. Rotate(G, asin((n_1 / n_2 * sin(α))), D_2) → G'
  11. Ray(D_2, G') → f
  12. Intersect(a, f) → H
  13. Segment(H, D_2) → g
  14. OrthogonalLine(H, a) → h
  15. Point(h) → I
  16. Angle(D_2, H, I) → γ
  17. Point(h) → J
  18. Rotate(J, (-asin((n_2 / n_1 * sin(γ)))), H) → J'
  19. Angle(J', H, J) → δ
  20. Ray(H, J') → i
  21. Segment(F, G) → j
  22. Segment(J, I) → k
  23. Angle(G, D_2, G') → β
  24. Rotate(G, asin((n_1 / (((1 + (0.002 * D)) * n_2)) * sin(α))), D_2) → P
  25. Rotate(G, asin((n_1 / (((1 + (0.004 * D)) * n_2)) * sin(α))), D_2) → Q
  26. Rotate(G, asin((n_1 / (((1 + (0.006 * D)) * n_2)) * sin(α))), D_2) → R
  27. Rotate(G, asin((n_1 / (((1 + (0.008 * D)) * n_2)) * sin(α))), D_2) → S
  28. Ray(D_2, P) → s
  29. Ray(D_2, Q) → t
  30. Ray(D_2, R) → a_1
  31. Ray(D_2, S) → b_1
  32. Rotate(G, asin((n_1 / (((1 + (0.01 * D)) * n_2)) * sin(α))), D_2) → T
  33. Ray(D_2, T) → c_1
  34. Intersect(a, s) → U
  35. Intersect(a, a_1) → V
  36. Intersect(a, t) → W
  37. Intersect(a, b_1) → Z
  38. Intersect(a, c_1) → A_1
  39. OrthogonalLine(U, a) → d_1
  40. OrthogonalLine(W, a) → e_1
  41. OrthogonalLine(V, a) → f_1
  42. OrthogonalLine(Z, a) → i_1
  43. OrthogonalLine(A_1, a) → l_1
  44. Point(d_1) → B_1
  45. Point(e_1) → C_1
  46. Point(f_1) → D_1
  47. Point(i_1) → E_1
  48. Point(l_1) → F_1
  49. Rotate(B_1, (-asin((((1 + (0.002 * D)) * n_2 / n_1) * sin(γ)))), U) → G_1
  50. Rotate(C_1, (-asin((((1 + (0.004 * D)) * n_2 / n_1) * sin(γ)))), W) → H_1
  51. Rotate(D_1, (-asin((((1 + (0.006 * D)) * n_2 / n_1) * sin(γ)))), V) → I_1
  52. Rotate(E_1, (-asin((((1 + (0.008 * D)) * n_2 / n_1) * sin(γ)))), Z) → J_1
  53. Rotate(F_1, (-asin((((1 + (0.01 * D)) * n_2 / n_1) * sin(γ)))), A_1) → K_1
  54. Ray(U, G_1) → n
  55. Ray(W, H_1) → p
  56. Ray(V, I_1) → q
  57. Ray(Z, J_1) → r
  58. Ray(A_1, K_1) → l
  59. Segment(D_2, U) → g_1
  60. Segment(D_2, V) → h_1
  61. Segment(D_2, Z) → j_1
  62. Segment(D_2, A_1) → k_1
  63. Segment(D_2, W) → m_1
  64. Intersect(b, a) → K
  65. Intersect(b, c) → L
  66. Intersect(a, c) → M
  67. Polygon(K, L, M) → poly2, m_2, k_2, l_2