MathPlotAI Logo MathPlotAI

Refraction and Total Internal Reflection

Refraction and Total Internal Reflection
Loading the math board and drawing, please wait…
2018-03-26 12:31
AngleTrigonometryGeometric Construction
This example demonstrates the phenomenon of refraction and total internal reflection of light. Key mathematical concepts include Snell's Law and the condition for total internal reflection. It uses GeoGebra commands such as Circle, Ray, Angle, Intersect, and Mirror for construction. Suitable for high school physics and mathematics education.

GeoGebra Commands & Parameters

  1. Circle((0, 0), 1) → c
  2. Point(c) → A
  3. If(y(A) ≥ 0, arg(A) - 90°, (-arg(A)) - 90°) → α
  4. If(y(A) ≥ 0, asin((n_1 * sin(α) / n_2)), asin((n_2 * sin(α) / n_1))) → β
  5. Ray(O, A) → f
  6. If(Defined[β], If[y(A) ≥ 0, (1; (-(90° - β))), (1; 90° - β)], Mirror[A, h]) → B
  7. Ray(O, B) → g
  8. If(n_2 > n_1, asind(n_1 / n_2), n_1 > n_2, asind(n_2 / n_1)) → critical
  9. If(n_2 > n_1, If[x(A) < 0, (1; -90° - critical), (1; -90° + critical)], n_1 > n_2, If[x(A) < 0, (1; 90° + critical), (1; 90° - critical)]) → criticalPoint
  10. If(y(A) ≥ 0, (0, 1), (0, -1)) → A'
  11. Angle(A, O, A') → γ
  12. If(y(B) ≥ 0, (0, 1), (0, -1)) → B'
  13. Angle(B, O, B') → δ
  14. Segment(A, O) → i
  15. Segment(O, B) → j
  16. Intersect(Circle[O, 0.5], AngularBisector[A, O, A'], 2) → A''
  17. Mirror(A, h) → C
  18. Ray(O, C) → k
  19. Segment(O, C) → l
  20. Intersect(Circle[O, 0.5], AngularBisector[B, O, B'], 2) → B''

AI Drawing Prompt Reference

Draw a unit circle centered at the origin with a horizontal diameter as the interface. Place a movable point on the circle; draw an incident ray from the center to this point. Using Snell's law, compute the refraction angle and draw the refracted ray; when the incident angle exceeds the critical angle, show the total internal reflection ray (i.e., the reflected ray). Label the incident angle, refraction angle, and critical angle with arcs. Also draw the normal (vertical diameter) and show symmetric auxiliary lines of the incident and refracted rays about the normal. The figure illustrates refraction and total internal reflection of light between two media.
The prompt above was compiled from the original drawing commands and is for reference only.