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Reflection and Refraction

Reflection and Refraction
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2020-07-26 17:34
AngleTransformationGeometric Construction
This example demonstrates the phenomena of reflection and refraction of light. Key mathematical concepts include angles, transformations, and geometric construction. Using GeoGebra commands such as Point, Segment, Rotate, and Mirror, the behavior of light in different media can be dynamically illustrated. Suitable for high school physics and mathematics courses.

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

Illustrate the reflection and refraction of light between two different media. Start with an initial light ray, then use rotation and reflection to show the reflected and refracted rays. Label the angles of incidence, reflection, and refraction, and display the different media. Use polygons to represent the boundaries and rays to indicate the direction of light propagation.
The prompt above was compiled from the original drawing commands and is for reference only.