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Refraction with Lens and Sphere

Refraction with Lens and Sphere
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2019-02-11 01:11
TrigonometryTransformationGeometric Construction
This example demonstrates the refraction phenomenon with lenses and spheres. Key mathematical concepts include geometric construction, transformation, and trigonometry. Using GeoGebra commands such as Mirror, Segment, and LineBisector, the refraction model of lenses and spheres is constructed. Suitable for high school physics and mathematics education.

GeoGebra Commands & Parameters

  1. Mirror(A, yAxis) → A'
  2. Mirror(C, xAxis) → C'
  3. Segment(C, A) → f
  4. LineBisector(f) → g
  5. Intersect(g, xAxis) → D
  6. CircleArc(D, C, C') → c
  7. Mirror(D, yAxis) → D'
  8. CircleArc(D', C', C) → d
  9. Intersect(c, g) → E,
  10. Line(E, xAxis) → h
  11. Angle(g, h) → α
  12. Intersect(h, yAxis) → F
  13. Distance(E, F) → EF
  14. Line(E, G) → i
  15. Intersect(d, i) → H,
  16. Line(D', H) → j
  17. Angle(i, j) → γ
  18. Segment(E, H) → k
  19. Angle(h, j) → ε
  20. Segment(H, Q) → l
  21. Mirror(E, xAxis) → E'
  22. Mirror(H, xAxis) → H'
  23. Segment(E', H') → k'
  24. Mirror(H, xAxis) → H'_1
  25. Mirror(Q, xAxis) → Q'
  26. Segment(H'_1, Q') → l'
  27. Mirror(h, xAxis) → h'