Geometric Construction of Light Reflection Inside an Ellipse
2019-08-14 06:33
This example demonstrates the geometric construction of light reflection inside an ellipse. Utilizing the optical property that light from one focus reflects to the other, it dynamically constructs incident and reflected rays using GeoGebra commands like Point, Ellipse, and Sequence, intuitively visualizing the optical characteristics of conic sections.
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\\" + (LaTeX[If[step ≥ 1, "(1)~构思：\\ 在椭圆上分布均匀地取点列作为反射点，\\ 右焦点作为起点，点例中的点作为终点构造向量，形成入射光线，\\ 点例中的点作为起点，左焦点作为终点构造向量，形成反射光线"]]) + "
\\
\\" + (LaTeX[If[step ≥ 2, "(2)~用基本命令绘制椭圆"]]) + "
\\
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\\
\\" + (LaTeX[If[step ≥ 4, " (4)~l1=Sequence(Point(c, i), i, 0, 1, a) \\ i表示点在椭圆c上的值，\\a表示间距步长，a越小，点取得越密。"]]) + "
\\
\\" + (LaTeX[If[step ≥ 5, " (5)~Zip(Vector(B, S), S, l1)\\ 映射命令表示将l1中的点映射给点S，\\点S再和右焦点B构造向量"]]) + "
\\
\\" + (LaTeX[If[step ≥ 6, " (6)~Zip(Vector(S, A), S, l1) \\制作过程参考了\\衡阳师院孟宝兴老师的课件，在此表示感谢！"]]) + """ />
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