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Reflection and Refraction by Michael Proudman

Reflection and Refraction by Michael Proudman
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2019-12-04 20:22
TriangleCircleAngleGeometric Construction
This example demonstrates the geometric construction of reflection and refraction phenomena. Key mathematical concepts include reflection laws, refraction laws, angles, triangles, and circles. Construction involves using GeoGebra commands such as Point, Segment, Rotate, Mirror, Angle, and Polygon, along with objects like points, line segments, angles, and polygons. Suitable for middle or high school mathematics education to understand geometric transformations and optical principles.

GeoGebra Commands & Parameters

  1. Point(xAxis) → C
  2. Segment(E, F) → b
  3. Rotate(B, a1, A) → B'
  4. Segment(B', A) → d
  5. Rotate(B', (-a1) - 3.14159 + asin((n1 * sin(a1) / n2)), A) → BR
  6. Mirror(B', b) → B''
  7. Angle(E, A, B') → α
  8. Angle(B'', A, E) → β
  9. Angle(F, A, BR) → γ
  10. Point(xAxis) → D
  11. Point(xAxis) → G
  12. Polygon(D, G, H, I) → poly1, d_1, g, h, i
  13. Polygon(D, J, K, G) → poly2, d_2, j, k, g_1
  14. Segment(D, G) → c
  15. Ray(A, B'') → a
  16. Ray(A, BR) → f
  17. Polygon(L_1, M_1, N_1, O_1) → poly3_1, l_1, m_1, n_1, o_1
  18. Polygon(L_3, M_3, N_3, O_3) → poly3_3, l_3, m_3, n_3, o_3
  19. Polygon(L_4, M_4, N_4, O_4) → poly3_2, l_2, m_2, n_2, o_2
  20. Polygon(L_5, M_5, N_5, O_5) → poly3_4, l_4, m_4, n_4, o_4
  21. Ray(B', A) → n
  22. Point(n) → P
  23. Angle(BR, A, P) → δ
  24. Angle(P, A, BR) → ε
  25. Textfield(n2) → inputBox1
  26. Textfield(n1) → inputBox2
  27. Textfield(a1) → inputBox3

AI Drawing Prompt Reference

This is a geometric figure demonstrating reflection and refraction phenomena. The figure includes points, line segments, angles, triangles, and circles. The construction process involves rotating points, mirroring them, and calculating angles to illustrate reflection and refraction laws. Circles and triangles are also included to explain optical principles. The construction order starts from basic points, then rotates and mirrors to generate new points, calculates angles, and finally combines them into the figure.
The prompt above was compiled from the original drawing commands and is for reference only.