4 Reflexion am ebenen Spiegel
Author: Markus Sesselmann

Ebener Spiegel

f

e

c

b

a

a

b

c

e

f

j

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Lichtquelle

Lichtquelle

Beschriftung

Lichtquelle

Lichtquelle

Lichtquelle

j

f

e

a

Wahrscheinlichkeit

Reflexion am ebenen Spiegel

Zu bewegende Objekte:
Lichtquelle, Detektor, Ebener Spiegel

Achtung!
Lichtquelle und Detektor müssen auf derselben Seite des Spiegels sein, um etwas zu sehen!

\begin{matrix}
In\ Polarkoordinaten\ (d.h. \ Vektor \ v = (Betrag;Winkel)):\
Vektor = (Amplitude;2\cdot\pi\cdot\frac{Weglänge}{\lambda})
\end{matrix}

Ein Vektor bei der Cornu-Spirale ist folgendermaßen definiert:

A = (25.441268124249923, -15.235751544448535)
O_{10}: (x(A), y(A))
Breite = 2.1 (slider from 0.1 to 3, step 0.1)
O_{01}: (x(A) - 9 * Breite, y(A))
O_{02}: (x(A) - 8 * Breite, y(A))
O_{03}: (x(A) - 7 * Breite, y(A))
O_{04}: (x(A) - 6 * Breite, y(A))
O_{05}: (x(A) - 5 * Breite, y(A))
O_{06}: (x(A) - 4 * Breite, y(A))
O_{07}: (x(A) - 3 * Breite, y(A))
O_{08}: (x(A) - 2 * Breite, y(A))
O_{09}: (x(A) - Breite, y(A))
Lichtquelle = (12.891528446874092, -38.895096837861985)
Detektor = (43.408654984755216, -38.68936340052796)
B = If((y(Lichtquelle) < y(A)) ∧ (y(Detektor) < y(A)) ∨ (y(Lichtquelle) > y(A)) ∧ (y(Detektor) > y(A)), Lichtquelle)
C = If((y(Lichtquelle) < y(A)) ∧ (y(Detektor) < y(A)) ∨ (y(Lichtquelle) > y(A)) ∧ (y(Detektor) > y(A)), Detektor)
a_{08} = Segment(O_{08}, B)
a_{07} = Segment(O_{07}, B)
a_{06} = Segment(O_{06}, B)
a_{05} = Segment(O_{05}, B)
a_{04} = Segment(O_{04}, B)
a_{03} = Segment(O_{03}, B)
a_{02} = Segment(O_{02}, B)
a_{01} = Segment(O_{01}, B)
b_{01} = Segment(C, O_{01})
b_{02} = Segment(C, O_{02})
b_{03} = Segment(C, O_{03})
b_{04} = Segment(C, O_{04})
b_{05} = Segment(C, O_{05})
b_{06} = Segment(C, O_{06})
b_{07} = Segment(C, O_{07})
b_{08} = Segment(C, O_{08})
Spiegel = Segment(O_{01}, O_{10})
a_{09} = Segment(O_{09}, B)
a_{10} = Segment(O_{10}, B)
b_{09} = Segment(C, O_{09})
b_{10} = Segment(C, O_{10})
Amplitude = 1.9 (slider from 0.1 to 2, step 0.1)
λ = 0.22 (slider from 0.1 to 0.22, step 0.01)
Lichtquelle_{λ1}: (x(Lichtquelle), y(Lichtquelle))
Lichtquelle_{λ2}: (x(Lichtquelle), y(Lichtquelle))
Lichtquelle_{λ3}: (x(Lichtquelle), y(Lichtquelle))
Lichtquelle_{λ4}: (x(Lichtquelle), y(Lichtquelle))
Lichtquelle_{λ5}: (x(Lichtquelle), y(Lichtquelle))
Lichtquelle_{λ6}: (x(Lichtquelle), y(Lichtquelle))
φ_{01}: 2 * π * (Distance[B, O_{01}] + Distance[O_{01}, C]) / λ
φ_{02}: 2 * π * (Distance[B, O_{02}] + Distance[O_{02}, C]) / λ
φ_{03}: 2 * π * (Distance[B, O_{03}] + Distance[O_{03}, C]) / λ
φ_{04}: 2 * π * (Distance[B, O_{04}] + Distance[O_{04}, C]) / λ
φ_{05}: 2 * π * (Distance[B, O_{05}] + Distance[O_{05}, C]) / λ
φ_{06}: 2 * π * (Distance[B, O_{06}] + Distance[O_{06}, C]) / λ
φ_{07}: 2 * π * (Distance[B, O_{07}] + Distance[O_{07}, C]) / λ
φ_{08}: 2 * π * (Distance[B, O_{08}] + Distance[O_{08}, C]) / λ
φ_{09}: 2 * π * (Distance[B, O_{09}] + Distance[O_{09}, C]) / λ
φ_{10}: 2 * π * (Distance[B, O_{10}] + Distance[O_{10}, C]) / λ
u_{01}: (Amplitude; φ_{01})
u_{02}: (Amplitude; φ_{02})
u_{03}: (Amplitude; φ_{03})
u_{04}: (Amplitude; φ_{04})
u_{06}: (Amplitude; φ_{06})
u_{05}: (Amplitude; φ_{05})
u_{07}: (Amplitude; φ_{07})
u_{08}: (Amplitude; φ_{08})
u_{09}: (Amplitude; φ_{09})
u_{10}: (Amplitude; φ_{10})
Cornu = (19.817887503786437, -0.08005499417503634)
v_{10} = Translate(u_{10}, Cornu)
C_{01} = Translate(Cornu, u_{10})
v_{09} = Translate(u_{09}, C_{01})
C_{02} = Translate(C_{01}, u_{09})
v_{08} = Translate(u_{08}, C_{02})
C_{03} = Translate(C_{02}, u_{08})
v_{07} = Translate(u_{07}, C_{03})
C_{04} = Translate(C_{03}, u_{07})
v_{06} = Translate(u_{06}, C_{04})
C_{05} = Translate(C_{04}, u_{06})
v_{05} = Translate(u_{05}, C_{05})
C_{06} = Translate(C_{05}, u_{05})
v_{04} = Translate(u_{04}, C_{06})
C_{07} = Translate(C_{06}, u_{04})
v_{03} = Translate(u_{03}, C_{07})
C_{08} = Translate(C_{07}, u_{03})
v_{02} = Translate(u_{02}, C_{08})
C_{09} = Translate(C_{08}, u_{02})
v_{01} = Translate(u_{01}, C_{09})
C_{10} = Translate(C_{09}, u_{01})
R = Vector(Cornu, C_{10})
Vieleck1, c_{10}, cornu, a, b, D, E = Polygon(C_{10}, Cornu, 4)
I: sqrt(R * R)
Vieleck2, c, d, e, f = Polygon((999.1897151036789, 954.9481597645403), (999.1897151036789, -1045.0518402354605), (-1000.8102848963211, -1045.0518402354605), (-1000.8102848963211, 954.9481597645403))
Text1: "Zeigerlänge = " + I + ""
FLäche: I^(2)
Text3: "Fläche = " + FLäche + ""