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Newton's Rings Between Spheres

Newton's Rings Between Spheres
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2015-05-27 14:26
FunctionTrigonometrySolid GeometryGeometric Construction
This example demonstrates the phenomenon of Newton's rings between spherical surfaces, dynamically showing the formation of interference fringes. Core mathematical concepts include spherical geometry, quadratic functions, sine functions, and conditional probability. Construction highlights involve GeoGebra commands and objects like Circle, If, Point, Segment, CircumcircleArc, Polygon, and Intersect, as detailed in the construction summary. Suitable for high school students and math enthusiasts studying wave optics and geometric modeling.

GeoGebra Commands & Parameters

  1. Circle(A, UpdateRadius) → UpdateCircle
  2. If((390 ≤ λ) ∧ (λ ≤ 440), (440 - λ) / 50, If[(440 < λ) ∧ (λ ≤ 510), 0, If[(510 < λ) ∧ (λ ≤ 570), (λ - 510) / 60, If[680 < λ, λ / 1000, 1]]]) → R
  3. If((390 ≤ λ) ∧ (λ ≤ 440), 0, If[(440 < λ) ∧ (λ ≤ 480), (λ - 440) / 40, If[(480 < λ) ∧ (λ ≤ 580), 1, If[(580 < λ) ∧ (λ ≤ 640), (640 - λ) / 60, If[680 < λ, λ / 1000, 0]]]]) → G
  4. If((390 ≤ λ) ∧ (λ ≤ 490), 1, If[(490 < λ) ∧ (λ ≤ 510), (510 - λ) / 20, If[680 < λ, λ / 1000, 0]]) → B
  5. Circle(C, 1.5) → c
  6. Point(c) → D
  7. Segment(D, C) → b
  8. Point(c) → E
  9. Segment(H, I) → f
  10. Segment(H_1, I_1) → u_1
  11. Segment(N, O) → g
  12. Segment(N, P) → i
  13. Circle(Q, S) → k
  14. Circle(Q, T) → p
  15. Point(k) → U
  16. Point(p) → V
  17. Point(k) → W
  18. Point(p) → Z
  19. CircumcircleArc(U, S, W) → r
  20. CircumcircleArc(V, T, Z) → t
  21. Point(r) → A_1
  22. Point(r) → B_1
  23. Point(r) → C_1
  24. Point(r) → D_1
  25. Point(r) → E_1
  26. Point(t) → F_1
  27. Point(t) → G_1
  28. Point(t) → J_1
  29. Point(t) → K_1
  30. Point(t) → L_1
  31. Point(t) → M_1
  32. Point(t) → N_1
  33. Polygon(V, U, N_1, M_1, L_1, K_1, T, J_1, G_1, F_1, A_1, B_1, S, C_1, D_1, E_1, W, Z) → poly2, v, z_1, n_1, m_1, l_1, k_1, t_1, j_1, g_1, f_1, u, a_1, b_1, s_1, c_1, d_1, e_1, w
  34. Intersect(r, u, 2) → F
  35. Segment(Q, F) → d
  36. Segment(H_2, I_2) → f_2