MathPlotAI Logo MathPlotAI

Prism Dispersion

Prism Dispersion
Loading the math board and drawing, please wait…
2015-03-19 23:27
AngleVectorSolid Geometry
This example demonstrates how a prism disperses light. Key concepts include light refraction and the geometry of a prism. Using GeoGebra commands such as Point, Intersect, Segment, etc., the path of light through the prism can be dynamically shown. Suitable for high school physics and mathematics education.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Intersect(xAxis, yAxis) → A
  3. Segment(C, A) → c
  4. Slope(c) → m_c
  5. Point(c) → D
  6. CircleSector(D, D - (Length[c] * (1, (-1) / m_c)), A) → k
  7. Segment(C, B) → b
  8. PointIn(k) → E
  9. Vector(E, D) → u
  10. Slope(b) → m_b
  11. Segment(D_{plus}, D_{minus}) → a
  12. Angle(E, D, D_{minus}) → da
  13. Rotate(D_{plus}, (db / 180 * π), D) → F
  14. Ray(D, F) → d
  15. Intersect(d, b) → G
  16. Segment(D, G) → e
  17. Segment(G_{minus}, G_{plus}) → f
  18. Angle(D, G, G_{minus}) → ga
  19. Rotate(G_{plus}, (((-gb)) / 180 * π), G) → H
  20. Vector(G, G + (Vector[G, H] / Length[Vector[G, H]] * Length[u])) → g
  21. Rotate(D_{plus}, (db2 / 180 * π), D) → I
  22. Ray(D, I) → h
  23. Intersect(h, b) → J
  24. Segment(J_{minus}, J_{plus}) → i
  25. Angle(D, J, J_{minus}) → ja
  26. Rotate(J_{plus}, (((-jb)) / 180 * π), J) → K
  27. Vector(J, J + (Vector[J, K] / Length[Vector[J, K]] * Length[u])) → w
  28. Segment(D, J) → j
  29. LaTeX("\text{Typically, longer wavelengths (redder) have lower indices of refraction.}") → text1

AI Drawing Prompt Reference

Draw a prism to demonstrate how light disperses through it, showing refraction and dispersion. Start by sketching the prism's outline, then trace a light ray entering the prism, refracting inside, and splitting into different colors upon exiting. Dynamically display the light path, labeling key angles and vectors to illustrate the principle of dispersion.
The prompt above was compiled from the original drawing commands and is for reference only.