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Reflection off Round Surface - Example 2 by Stephen Jull

Reflection off Round Surface - Example 2 by Stephen Jull
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2015-04-21 21:23
CircleVectorGeometric Construction
This example demonstrates the reflection of light off a round surface. Key mathematical concepts include reflection, circle, vector, and line segment. It is constructed using GeoGebra commands such as Circle, Tangent, OrthogonalLine, Vector, Mirror, and Segment. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Circle(B, C) → c
  2. Tangent(C, c) → a,
  3. OrthogonalLine(C, a) → b
  4. Vector(A, C) → u
  5. Mirror(A, b) → A'
  6. Vector(C, A') → v
  7. Segment(A, A') → d
  8. Intersect(b, d) → D
  9. Angle(A, C, D) → α
  10. Angle(D, C, A') → β

AI Drawing Prompt Reference

Draw a circle c centered at point C. Draw a tangent a to circle c at point C, then draw the perpendicular line b to a. Draw a vector u from point A to point C, then reflect point A over line b to get point A'. Draw a vector v from point C to point A', and a line segment d from A to A'. Find the intersection point D of line segment d and perpendicular line b. Finally, measure angles ACD and DCA'.
The prompt above was compiled from the original drawing commands and is for reference only.