6 Lichtwege
Author: Markus Sesselmann

Lichtquelle

c

b

a

a

e

Lichtweg_a

Lichtweg_c

Lichtweg_e

Lichtquelle

Lichtquelle

Lichtquelle

Lichtquelle

Lichtquelle

b

c

d

Lichtweg_b

Lichtweg_d

d

e

Wahrscheinlichkeit

Wahrscheinlichkeit

e

Wahrscheinlichkeit

Wahrscheinlichkeit

d

e

Wahrscheinlichkeit

Wahrscheinlichkeit

e

Wahrscheinlichkeit

Wahrscheinlichkeit

c

d

e

Wahrscheinlichkeit

Wahrscheinlichkeit

e

Wahrscheinlichkeit

Wahrscheinlichkeit

d

e

Wahrscheinlichkeit

Wahrscheinlichkeit

e

Wahrscheinlihckeit

Wahrscheinlichkeit

b

c

d

e

Wahrscheinlichkeit

Wahrscheinlichkeit

e

Wahrscheinlichkeit

Wahrscheinlichkeit

d

e

Wahrscheinlichkeit

Wahrscheinlichkeit

e

Wahrscheinlichkeit

Wahrscheinlichkeit

c

d

e

Wahrscheinlichkeit

Wahrscheinlichkeit

e

Wahrscheinlichkeit

Wahrscheinlichkeit

Fläche = 0

d

e

Wahrscheinlichkeit

Wahrscheinlichkeit

e

Wahrscheinlichkeit

Lichtwege

Klicke einzelne Lichtwege weg und beobachte die Veränderung an der Cornu-Spirale!
Zu bewegendes Objekt:
Detektor

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

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

Lichtquelle_{λ1} = (-6, 0)
Amplitude = 500 (slider from 200 to 500, step 50)
λ = 0.12 (slider from 0.1 to 0.22, step 0.01)
Cornu = (16.4393403071973, 5.936521896147856)
AbstandMitte = 6 (slider from 4 to 6, step 0.1)
A' = (6, -10)
A = (6, 10)
Schirm = Segment(A, A')
Detektor = Point(Schirm)
Lichtquelle = (-6, 0)
O_3: (1 / 2 * (x(Lichtquelle) + x(Detektor)), 1 / 2 * (y(Lichtquelle) + y(Detektor)))
O_2: (x(O_3), y(O_3) - 1 / 2 * AbstandMitte)
b_2 = Segment(O_2, Detektor)
a_2 = Segment(O_2, Lichtquelle_{λ1})
φ_2: 2 * π * (a_2 + b_2) / λ
u_2: (Amplitude / (a_2 + b_2)^(2); φ_2)
O_1: (x(O_3), y(O_3) - 3 / 2 * AbstandMitte)
b_1 = Segment(O_1, Detektor)
a_1 = Segment(O_1, Lichtquelle)
φ_1: 2 * π * (a_1 + b_1) / λ
u_1: (Amplitude / (a_1 + b_1)^(2); φ_1)
v_{abcde}1 = Translate(u_1, Cornu)
C_{abcde}1 = Translate(Cornu, v_{abcde}1)
Vieleck1, a, b, c, d = Polygon((1000, 1000), (-1000, 1000), (-1000, -1000), (1000, -1000))
a_3 = Segment(O_3, Lichtquelle)
b_3 = Segment(O_3, Detektor)
O_5: (x(O_3), y(O_3) + 3 / 2 * AbstandMitte)
b_5 = Segment(Detektor, O_5)
a_5 = Segment(O_5, Lichtquelle)
φ_3: 2 * π * (a_3 + b_3) / λ
φ_5: 2 * π * (a_5 + b_5) / λ
u_3: (Amplitude / (a_3 + b_3)^(2); φ_3)
u_5: (Amplitude / (a_5 + b_5)^(2); φ_5)
C = (0, 20)
C' = Mirror(C, xAxis)
e = Segment(C, C')
W1 = true
W3 = true
W5 = true
B = (-36, 10)
B' = (-29, 10)
B''' = (-36, -6)
B'''' = (-29, -6)
Vieleck2, b_{10}, b''', b'''', b' = Polygon(B, B''', B'''', B')
Lichtquelle_{λ2} = (-6, 0)
Lichtquelle_{λ3} = (-6, 0)
Lichtquelle_{λ4} = (-6, 0)
Lichtquelle_{λ5} = (-6, 0)
Lichtquelle_{λ6} = (-6, 0)
v_{abcde}2 = Translate(u_2, C_{abcde}1)
C_{abcde}2 = Translate(C_{abcde}1, v_{abcde}2)
v_{abcde}3 = Translate(u_3, C_{abcde}2)
C_{abcde}3 = Translate(C_{abcde}2, v_{abcde}3)
Z = (-18, 0)
Z' = (18, 0)
c_1 = Segment(Z, Z')
O_4: (x(O_3), y(O_3) + 1 / 2 * AbstandMitte)
a_4 = Segment(O_4, Lichtquelle_{λ1})
b_4 = Segment(Detektor, O_4)
W2 = true
W4 = true
φ_4: 2 * π * (a_4 + b_4) / λ
u_4: (Amplitude / (a_4 + b_4)^(2); φ_4)
v_{abcde}4 = Translate(u_4, C_{abcde}3)
C_{abcde}4 = Translate(C_{abcde}3, v_{abcde}4)
v_{abcde}5 = Translate(u_5, C_{abcde}4)
C_{abcde}5 = Translate(C_{abcde}4, v_{abcde}5)
R_{abcde} = Vector(Cornu, C_{abcde}5)
Vieleck_{abcde}, cornu, c_{abcde}5, f, g, D, E = Polygon(Cornu, C_{abcde}5, 4)
R_{abcd} = Vector(Cornu, C_{abcde}4)
Vieleck_{abcd}, cornu_1, c_{abcde}4, h, i, F, G = Polygon(Cornu, C_{abcde}4, 4)
W_{abcde}: R_{abcde} * R_{abcde}
Text1: "Fläche = " + W_{abcde} + ""
W_{abcd}: R_{abcd} * R_{abcd}
Text2: "Fläche = " + W_{abcd} + ""
v_{abce}5 = Translate(u_5, C_{abcde}3)
C_{abce}4 = Translate(C_{abcde}3, v_{abce}5)
R_{abce} = Vector(Cornu, C_{abce}4)
Vieleck_{abce}, c_{abce}4, cornu_2, j, k, H, I = Polygon(C_{abce}4, Cornu, 4)
W_{abce}: R_{abce} * R_{abce}
Text3: "Fläche = " + W_{abce} + ""
R_{abc} = Vector(Cornu, C_{abcde}3)
Vieleck_{abc}, c_{abcde}3, cornu_3, l, m, J, K = Polygon(C_{abcde}3, Cornu, 4)
W_{abc}: R_{abc} * R_{abc}
Text4: "Fläche = " + W_{abc} + ""
v_{abde}4 = Translate(u_4, C_{abcde}2)
C_{abde}3 = Translate(C_{abcde}2, v_{abde}4)
v_{abde}5 = Translate(u_5, C_{abde}3)
C_{abde}4 = Translate(C_{abde}3, v_{abde}5)
R_{abde} = Vector(Cornu, C_{abde}4)
Vieleck_{abde}, c_{abde}4, cornu_4, n, p, L, M = Polygon(C_{abde}4, Cornu, 4)
W_{abde}: R_{abde} * R_{abde}
Text5: "Fläche = " + W_{abde} + ""
R_{abd} = Vector(Cornu, C_{abde}3)
Vieleck_{abd}, c_{abde}3, cornu_5, q, r, N, O = Polygon(C_{abde}3, Cornu, 4)
W_{abd}: R_{abd} * R_{abd}
Text6: "Fläche = " + W_{abd} + ""
v_{abe}5 = Translate(u_5, C_{abcde}2)
C_{abe}3 = Translate(C_{abcde}2, v_{abe}5)
R_{abe} = Vector(Cornu, C_{abe}3)
Vieleck_{abe}, c_{abe}3, cornu_6, s, t, P, Q = Polygon(C_{abe}3, Cornu, 4)
W_{abe}: R_{abe} * R_{abe}
Text7: "Fläche = " + W_{abe} + ""
R_{ab} = Vector(Cornu, C_{abcde}2)
Vieleck_{ab}, c_{abcde}2, cornu_7, d_1, e_1, R, S = Polygon(C_{abcde}2, Cornu, 4)
W_{ab}: R_{ab} * R_{ab}
Text8: "Fläche = " + W_{ab} + ""
v_{acde}3 = Translate(u_3, C_{abcde}1)
C_{acde}2 = Translate(C_{abcde}1, v_{acde}3)
v_{acde}4 = Translate(u_4, C_{acde}2)
C_{acde}3 = Translate(C_{acde}2, v_{acde}4)
v_{acde}5 = Translate(u_5, C_{acde}3)
C_{acde}4 = Translate(C_{acde}3, v_{acde}5)
R_{acde} = Vector(Cornu, C_{acde}4)
Vieleck_{acde}, c_{acde}4, cornu_8, f_1, g_1, T, U = Polygon(C_{acde}4, Cornu, 4)
W_{acde}: R_{acde} * R_{acde}
Text9: "Fläche = " + W_{acde} + ""
R_{acd} = Vector(Cornu, C_{acde}3)
Vieleck_{acd}, c_{acde}3, cornu_9, h_1, i_1, V, W = Polygon(C_{acde}3, Cornu, 4)
W_{acd}: R_{acd} * R_{acd}
Text10: "Fläche = " + W_{acd} + ""
v_{ace}5 = Translate(u_5, C_{acde}2)
C_{ace}3 = Translate(C_{acde}2, v_{ace}5)
R_{ace} = Vector(Cornu, C_{ace}3)
Vieleck_{ace}, c_{ace}3, cornu_{10}, j_1, k_1, A_1, B_1 = Polygon(C_{ace}3, Cornu, 4)
W_{ace}: R_{ace} * R_{ace}
Text11: "Fläche = " + W_{ace} + ""
R_{ac} = Vector(Cornu, C_{acde}2)
Vieleck_{ac}, c_{acde}2, cornu_{11}, l_1, m_1, C_1, D_1 = Polygon(C_{acde}2, Cornu, 4)
W_{ac}: R_{ac} * R_{ac}
Text12: "Fläche = " + W_{ac} + ""
v_{ade}4 = Translate(u_4, C_{abcde}1)
C_{ade}2 = Translate(C_{abcde}1, v_{ade}4)
v_{ade}5 = Translate(u_5, C_{ade}2)
C_{ade}3 = Translate(C_{ade}2, v_{ade}5)
R_{ade} = Vector(Cornu, C_{ade}3)
Vieleck_{ade}, c_{ade}3, cornu_{12}, n_1, p_1, E_1, F_1 = Polygon(C_{ade}3, Cornu, 4)
W_{ade}: R_{ade} * R_{ade}
Text13: "Fläche = " + W_{ade} + ""
R_{ad} = Vector(Cornu, C_{ade}2)
Vieleck_{ad}, c_{ade}2, cornu_{13}, q_1, r_1, G_1, H_1 = Polygon(C_{ade}2, Cornu, 4)
W_{ad}: R_{ad} * R_{ad}
Text14: "Fläche = " + W_{ad} + ""
v_{ae}5 = Translate(u_5, C_{abcde}1)
C_{ae}2 = Translate(C_{abcde}1, v_{ae}5)
R_{ae} = Vector(Cornu, C_{ae}2)
Vieleck_ae, c_{ae}2, cornu_{14}, s_1, t_1, I_1, J_1 = Polygon(C_{ae}2, Cornu, 4)
W_{ae}: R_{ae} * R_{ae}
Text15: "Fläche = " + W_{ae} + ""
R_{a} = Vector(Cornu, C_{abcde}1)
Vieleck_a, c_{abcde}1, cornu_{15}, c_2, d_2, K_1, L_1 = Polygon(C_{abcde}1, Cornu, 4)
W_{a}: R_{a} * R_{a}
Text16: "Fläche = " + W_{a} + ""
v_{bcde}2 = Translate(u_2, Cornu)
C_{bcde}1 = Translate(Cornu, v_{bcde}2)
v_{bcde}3 = Translate(u_3, C_{bcde}1)
C_{bcde}2 = Translate(C_{bcde}1, v_{bcde}3)
v_{bcde}4 = Translate(u_4, C_{bcde}2)
C_{bcde}3 = Translate(C_{bcde}2, v_{bcde}4)
v_{bcde}5 = Translate(u_5, C_{bcde}3)
C_{bcde}4 = Translate(C_{bcde}3, v_{bcde}5)
R_{bcde} = Vector(Cornu, C_{bcde}4)
Vieleck_{bcde}, c_{bcde}4, cornu_{16}, e_2, f_2, M_1, N_1 = Polygon(C_{bcde}4, Cornu, 4)
W_{bcde}: R_{bcde} * R_{bcde}
Text17: "Fläche = " + W_{bcde} + ""
R_{bcd} = Vector(Cornu, C_{bcde}3)
Vieleck_{bcd}, c_{bcde}3, cornu_{17}, g_2, h_2, P_1, Q_1 = Polygon(C_{bcde}3, Cornu, 4)
W_{bcd}: R_{bcd} * R_{bcd}
Text18: "Fläche = " + W_{bcd} + ""
v_{bce}5 = Translate(u_5, C_{bcde}2)
C_{bce}3 = Translate(C_{bcde}2, v_{bce}5)
R_{bce} = Vector(Cornu, C_{bce}3)
Vieleck_{bce}, c_{bce}3, cornu_{18}, i_2, j_2, R_1, S_1 = Polygon(C_{bce}3, Cornu, 4)
W_{bce}: R_{bce} * R_{bce}
Text19: "Fläche = " + W_{bce} + ""
R_{bc} = Vector(Cornu, C_{bcde}2)
Vieleck_{bc}, c_{bcde}2, cornu_{19}, k_2, l_2, T_1, U_1 = Polygon(C_{bcde}2, Cornu, 4)
W_{bc}: R_{bc} * R_{bc}
Text20: "Fläche = " + W_{bc} + ""
v_{bde}4 = Translate(u_4, C_{bcde}1)
C_{bde}2 = Translate(C_{bcde}1, v_{bde}4)
v_{bde}5 = Translate(u_5, C_{bde}2)
C_{bde}3 = Translate(C_{bde}2, v_{bde}5)
R_{bde} = Vector(Cornu, C_{bde}3)
Vieleck_{bde}, c_{bde}3, cornu_{20}, m_2, n_2, V_1, W_1 = Polygon(C_{bde}3, Cornu, 4)
W_{bde}: R_{bde} * R_{bde}
Text21: "Fläche = " + W_{bde} + ""
R_{bd} = Vector(Cornu, C_{bde}2)
Vieleck_{bd}, c_{bde}2, cornu_{21}, p_2, q_2, Z_1, A_2 = Polygon(C_{bde}2, Cornu, 4)
W_{bd}: R_{bd} * R_{bd}
Text22: "Fläche = " + W_{bd} + ""
v_{be}5 = Translate(u_5, C_{bcde}1)
C_{be}2 = Translate(C_{bcde}1, v_{be}5)
R_{be} = Vector(Cornu, C_{be}2)
Vieleck_{be}, c_{be}2, cornu_{22}, r_2, s_2, B_2, C_2 = Polygon(C_{be}2, Cornu, 4)
W_{be}: R_{be} * R_{be}
Text23: "Fläche = " + W_{be} + ""
R_{b} = Vector(Cornu, C_{bcde}1)
Vieleck_{b}, c_{bcde}1, cornu_{23}, t_2, c_3, D_2, E_2 = Polygon(C_{bcde}1, Cornu, 4)
W_{b}: R_{b} * R_{b}
Text24: "Fläche = " + W_{b} + ""
v_{cde}3 = Translate(u_3, Cornu)
C_{cde}1 = Translate(Cornu, v_{cde}3)
v_{cde}4 = Translate(u_4, C_{cde}1)
C_{cde}2 = Translate(C_{cde}1, v_{cde}4)
v_{cde}5 = Translate(u_5, C_{cde}2)
C_{cde}3 = Translate(C_{cde}2, v_{cde}5)
R_{cde} = Vector(Cornu, C_{cde}3)
Vieleck_{cde}, cornu_{24}, c_{cde}3, d_3, e_3, F_2, G_2 = Polygon(Cornu, C_{cde}3, 4)
W_{cde}: R_{cde} * R_{cde}
Text25: "Fläche = " + W_{cde} + ""
R_{cd} = Vector(Cornu, C_{cde}2)
Vieleck_{cd}, c_{cde}2, cornu_{25}, f_3, g_3, H_2, I_2 = Polygon(C_{cde}2, Cornu, 4)
W_{cd}: R_{cd} * R_{cd}
Text26: "Fläche = " + W_{cd} + ""
v_{ce}5 = Translate(u_5, C_{cde}1)
C_{ce}2 = Translate(C_{cde}1, v_{ce}5)
R_{ce} = Vector(Cornu, C_{ce}2)
Vieleck_{ce}, c_{ce}2, cornu_{26}, h_3, i_3, J_2, K_2 = Polygon(C_{ce}2, Cornu, 4)
W_{ce}: R_{ce} * R_{ce}
Text27: "Fläche = " + W_{ce} + ""
R_{c} = Vector(Cornu, C_{cde}1)
Vieleck_{c}, c_{cde}1, cornu_{27}, j_3, k_3, L_2, M_2 = Polygon(C_{cde}1, Cornu, 4)
W_{c}: R_{c} * R_{c}
Text28: "Fläche = " + W_{c} + ""
v_{de}4 = Translate(u_4, Cornu)
C_{de}1 = Translate(Cornu, v_{de}4)
v_{de}5 = Translate(u_5, C_{de}1)
C_{de}2 = Translate(C_{de}1, v_{de}5)
R_{de} = Vector(Cornu, C_{de}2)
Vieleck_{de}, c_{de}2, cornu_{28}, l_3, m_3, N_2, P_2 = Polygon(C_{de}2, Cornu, 4)
W_{de}: R_{de} * R_{de}
Text30: "Fläche = " + W_{de} + ""
R_{d} = Vector(Cornu, C_{de}1)
W_{d}: R_{d} * R_{d}
Vieleck_{d}, c_{de}1, cornu_{29}, n_3, p_3, Q_2, R_2 = Polygon(C_{de}1, Cornu, 4)
Text31: "Fläche = " + W_{d} + ""
v_{e}5 = Translate(u_5, Cornu)
C_{e}1 = Translate(Cornu, v_{e}5)
R_{e} = Vector(Cornu, C_{e}1)
Vieleck_{e}, c_{e}1, cornu_{30}, q_3, r_3, S_2, T_2 = Polygon(C_{e}1, Cornu, 4)
W_{e}: R_{e} * R_{e}
Text32: "Fläche = " + W_{e} + ""