7 Linse
Author: Markus Sesselmann

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Resultierende

Wahrscheinlichkeit

Linse

Verändere den Krümmungsradius und beobachte die Veränderungen an der Cornu-Spirale!

Ein Vektor bei der Cornu-Spirale ist wie folgt definiert:

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

Amplitude = 0.4 (slider from 0.1 to 0.4, step 0.01)
Krümmungsradius = 3.5 (slider from 1.7 to 3.8, step 0.1)
A = (0, 1)
d_2 = Circle(A, Krümmungsradius)
B = (0, -1)
c = Circle(B, Krümmungsradius)
F2, F1 = Intersect(d_2, c)
O6: (-(Krümmungsradius + x(F1)), 0)
O6' = Mirror(O6, yAxis)
O6'': (1 / 2 * (x(O6) + x(O6')), 0)
O11'': (x(O6''), y(O6'') + 1)
O1'' = Mirror(O11'', xAxis)
Lichtquelle: (x(F1), 0)
λ = 0.22 (slider from 0.1 to 0.22, step 0.01)
C1': (-1, y(O1''))
n = Segment(O1'', C1')
C11': (-1, y(O11''))
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))
e = Circle(F1, Krümmungsradius)
f = Circle(F2, Krümmungsradius)
Dicke: 2 * Krümmungsradius - x(F2) + x(F1)
Text5: "Dicke der Linse ist " + Dicke + ""
a = Segment(A, B)
C = Point(a)
C': (-1, y(C))
b = Segment(C', C)
E = Intersect(f, b)
Ortslinie1 = Locus(E, C)
C'': (1, y(C))
g = Segment(C, C'')
F = Intersect(e, g)
Ortslinie2 = Locus(F, C)
O10'': (x(O6''), y(O6'') + 0.8)
O2'' = Mirror(O10'', xAxis)
C10': (-1, y(O10''))
h = Segment(O10'', C10')
O10 = Intersect(f, h)
C2': (-1, y(O2''))
i = Segment(O2'', C2')
O2 = Intersect(f, i)
j = Segment(F2, O6'')
Vieleck1, c_{10}, d_1, e_1, f_1 = Polygon((-1000, -1000), (-1000, 1000), (1000, 1000), (1000, -1000))
O9'': (x(O6''), y(O6'') + 0.6)
O8'': (x(O6''), y(O6'') + 0.4)
O7'': (x(O6''), y(O6'') + 0.2)
O5'': (x(O6''), y(O6'') - 0.2)
O4'': (x(O6''), y(O6'') - 0.4)
O3'': (x(O6''), y(O6'') - 0.6)
O2' = Mirror(O2, yAxis)
O10' = Mirror(O10, yAxis)
C3': (-1, y(O3''))
d = Segment(O3'', C3')
O3 = Intersect(f, d)
O3' = Mirror(O3, yAxis)
C4': (-1, y(O4''))
k = Segment(C4', O4'')
O4 = Intersect(f, k)
O4' = Mirror(O4, yAxis)
C5': (-1, y(O5''))
l = Segment(C5', O5'')
O5 = Intersect(f, l)
O5' = Mirror(O5, yAxis)
C7': (-1, y(O7''))
m = Segment(C7', O7'')
O7 = Intersect(f, m)
O7' = Mirror(O7, yAxis)
C8': (-1, y(O8''))
p = Segment(O8'', C8')
O8 = Intersect(f, p)
O8' = Mirror(O8, yAxis)
C9': (-1, y(O9''))
q = Segment(O9'', C9')
O9 = Intersect(f, q)
O9' = Mirror(O9, yAxis)
a_11 = Segment(O11'', Lichtquelle_{λ1})
a_10 = Segment(O10, Lichtquelle_{λ1})
a_9 = Segment(O9, Lichtquelle_{λ1})
a_8 = Segment(O8, Lichtquelle_{λ1})
a_7 = Segment(O7, Lichtquelle_{λ1})
a_6 = Segment(O6, Lichtquelle_{λ1})
a_5 = Segment(O5, Lichtquelle_{λ1})
a_4 = Segment(O4, Lichtquelle_{λ1})
a_3 = Segment(O3, Lichtquelle_{λ1})
a_2 = Segment(O2, Lichtquelle_{λ1})
a_1 = Segment(O1'', Lichtquelle_{λ1})
b_10 = Segment(O10, O10')
b_9 = Segment(O9, O9')
b_8 = Segment(O8, O8')
b_7 = Segment(O7, O7')
b_6 = Segment(O6, O6')
b_5 = Segment(O5, O5')
b_4 = Segment(O4, O4')
b_3 = Segment(O3, O3')
b_2 = Segment(O2, O2')
c_2 = Segment(F2, O2')
c_1 = Segment(O1'', F2)
c_11 = Segment(O11'', F2)
c_10 = Segment(O10', F2)
c_9 = Segment(O9', F2)
c_3 = Segment(O3', F2)
c_4 = Segment(O4', F2)
c_5 = Segment(O5', F2)
c_6 = Segment(O6', F2)
c_7 = Segment(O7', F2)
c_8 = Segment(O8', F2)
Cornu = (2.2896226589514486, 2.1819959304771466)
φ_{1}: 2 * π * (Distance[F1, O1''] + Distance[O1'', F2]) / λ
φ_{2}: 2 * π * (Distance[F1, O2] + Distance[O2, O2'] + Distance[O2', F2]) / λ
φ_{3}: 2 * π * (Distance[F1, O3] + Distance[O3, O3'] + Distance[O3', F2]) / λ
φ_{4}: 2 * π * (Distance[F1, O4] + Distance[O4, O4'] + Distance[O4', F2]) / λ
φ_{5}: 2 * π * (Distance[F1, O5] + Distance[O5, O5'] + Distance[O5', F2]) / λ
φ_{6}: 2 * π * (Distance[F1, O6] + Distance[O6, O6'] + Distance[O6', F2]) / λ
φ_{7}: 2 * π * (Distance[F1, O7] + Distance[O7, O7'] + Distance[O7', F2]) / λ
φ_{8}: 2 * π * (Distance[F1, O8] + Distance[O8, O8'] + Distance[O8', F2]) / λ
φ_{9}: 2 * π * (Distance[F1, O9] + Distance[O9, O9'] + Distance[O9', F2]) / λ
φ_{10}: 2 * π * (Distance[F1, O10] + Distance[O10, O10'] + Distance[O10', F2]) / λ
φ_{11}: 2 * π * (Distance[F1, O11''] + Distance[O11'', F2]) / λ
u_{1}: (Amplitude; φ_{1})
u_{2}: (Amplitude; φ_{2})
u_{3}: (Amplitude; φ_{3})
u_{4}: (Amplitude; φ_{4})
u_{5}: (Amplitude; φ_{5})
u_{6}: (Amplitude; φ_{6})
u_{7}: (Amplitude; φ_{7})
u_{8}: (Amplitude; φ_{8})
u_{9}: (Amplitude; φ_{9})
u_{10}: (Amplitude; φ_{10})
u_{11}: (Amplitude; φ_{11})
v_{1} = Translate(u_{1}, Cornu)
C_{1} = Translate(Cornu, v_{1})
v_{2} = Translate(u_{2}, C_{1})
C_{2} = Translate(C_{1}, v_{2})
v_{3} = Translate(u_{3}, C_{2})
C_{3} = Translate(C_{2}, v_{3})
v_{4} = Translate(u_{4}, C_{3})
C_{4} = Translate(C_{3}, v_{4})
v_{5} = Translate(u_{5}, C_{4})
C_{5} = Translate(C_{4}, v_{5})
v_{6} = Translate(u_{6}, C_{5})
C_{6} = Translate(C_{5}, v_{6})
v_{7} = Translate(u_{7}, C_{6})
C_{7} = Translate(C_{6}, v_{7})
v_{8} = Translate(u_{8}, C_{7})
C_{8} = Translate(C_{7}, v_{8})
v_{9} = Translate(u_{9}, C_{8})
C_{9} = Translate(C_{8}, v_{9})
v_{10} = Translate(u_{10}, C_{9})
C_{10} = Translate(C_{9}, v_{10})
v_{11} = Translate(u_{11}, C_{10})
C_{11} = Translate(C_{10}, v_{11})
R = Vector(Cornu, C_{11})
Länge_R = Distance(Cornu, C_{11})
Text1: "Zeigerlänge = " + Länge_R + ""
Vieleck2, cornu, c_{11}, r, s, D, G = Polygon(Cornu, C_{11}, 4)
Fläche: Länge_R^(2)
Text2: "Fläche = " + Fläche + ""