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Reflection and Refraction for iPad

Reflection and Refraction for iPad
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2013-04-19 22:37
AngleTransformationGeometric Construction
This example demonstrates the phenomena of reflection and refraction. Key mathematical concepts include angles, transformations, and geometric construction. Using GeoGebra commands such as Point, Segment, Rotate, and Mirror, the path of light can be dynamically shown. Suitable for high school physics and mathematics education.

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

Draw the reflection and refraction of a light ray between two media, highlighting key angles and transformations. Start with an initial light ray, then use rotation and reflection to show the reflected and refracted rays. Label the incident, reflected, and refracted angles, and dynamically display the light path. Use polygons and rays to represent the light paths and angle relationships, suitable for physics and mathematics education.
The prompt above was compiled from the original drawing commands and is for reference only.