Δs/2

Δs/2

Zeiger

Welle

Geometrie

2. Ebene

3. Ebene

4. Ebene

5. Ebene

Bragg - Reflexion

U. Konrad; 2013

Die Längenangaben erfolgen
dimensionslos in L.E.

Δs = 2·d·sin(β)

d

ß

Netzebenenabstand

β = 0.3508111796508603 rad (slider from 0.1*° to 89.9*°, step 0.1*°)
NE0 = (0, 0)
d = 2 (slider from 1 to 4, step 0.01)
NE20: (0, -d)
NER1: (d, 0)
NER1' = Mirror(NER1, yAxis)
NER1'' = Rotate(NER1', -β, NE0)
e = Ray(NE0, NER1'')
j = Line(NE20, e)
q = OrthogonalLine(NE0, j)
F = Intersect(j, q)
s1 = Segment(F, NE20)
amp = 1 (slider from 0.3 to 1.5, step 0.1)
λ = 1.36 (slider from 0.1 to 3, step 0.01)
f(x) = amp * sin(x * 2 * π / λ)
Ebenen = 3 (slider from 1 to 5, step 1)
a = true
b = true
c = false
NER2: (2 * d, 0)
NER3: (3 * d, 0)
NER4: (4 * d, 0)
NER5: (5 * d, 0)
NER2' = Mirror(NER2, yAxis)
NER3' = Mirror(NER3, yAxis)
NER4' = Mirror(NER4, yAxis)
NER5' = Mirror(NER5, yAxis)
NER21: (d, -d)
NER22: (2 * d, -d)
NER23: (3 * d, -d)
NER24: (4 * d, -d)
NER25: (5 * d, -d)
NE30: (0, -2 * d)
NER31: (d, -2 * d)
NER32: (2 * d, -2 * d)
NER33: (3 * d, -2 * d)
NER34: (4 * d, -2 * d)
NER35: (5 * d, -2 * d)
NE40: (0, -3 * d)
NER41: (d, -3 * d)
NER42: (2 * d, -3 * d)
NER43: (3 * d, -3 * d)
NER44: (4 * d, -3 * d)
NER45: (5 * d, -3 * d)
NE50: (0, -4 * d)
NER51: (d, -4 * d)
NER52: (2 * d, -4 * d)
NER53: (3 * d, -4 * d)
NER54: (4 * d, -4 * d)
NER55: (5 * d, -4 * d)
NER21' = Mirror(NER21, yAxis)
NER22' = Mirror(NER22, yAxis)
NER23' = Mirror(NER23, yAxis)
NER24' = Mirror(NER24, yAxis)
NER25' = Mirror(NER25, yAxis)
NER35' = Mirror(NER35, yAxis)
NER34' = Mirror(NER34, yAxis)
NER33' = Mirror(NER33, yAxis)
NER32' = Mirror(NER32, yAxis)
NER31' = Mirror(NER31, yAxis)
NER41' = Mirror(NER41, NE40)
NER42' = Mirror(NER42, NE40)
NER43' = Mirror(NER43, NE40)
NER44' = Mirror(NER44, NE40)
NER45' = Mirror(NER45, NE40)
NER55' = Mirror(NER55, NE50)
NER54' = Mirror(NER54, NE50)
NER53' = Mirror(NER53, NE50)
NER52' = Mirror(NER52, NE50)
NER51' = Mirror(NER51, NE50)
NE0' = Mirror(NE0, NER55')
β_1 = Angle(NER1'', NE0, NER1')
NER1'_1 = Rotate(NER1, β, NE0)
γ = Angle(NER1, NE0, NER1'_1)
g = AngularBisector(NER1'', NE0, NER1')
h = Function(-f(x), -6 * d, 0)
A = Point(h)
A' = Mirror(A, g)
Ortslinie1 = Locus(A', A)
i = Ray(NE0, NER1'_1)
k = Line(NE30, j)
l = Line(NE40, k)
m = Line(NE50, l)
WFl: (-6 * d, 0)
WFl' = Mirror(WFl, g)
n = OrthogonalLine(WFl', e)
B = Intersect(j, n)
C = Intersect(k, n)
D = Intersect(l, n)
E = Intersect(n, m)
G = Intersect(k, q)
H = Intersect(l, q)
I = Intersect(m, q)
s2 = Segment(G, NE30)
s3 = Segment(H, NE40)
s4 = Segment(I, NE50)
p = Function(-f(x + s1) - d, -6 * d - s1, 0)
r = Function(-f(x + s2) - 2 * d, -6 * d - s2, 0)
s = AngularBisector(NER21', NE20, B)
J = Point(p)
J' = Mirror(J, s)
Ortslinie2 = Locus(J', J)
K = Point(r)
t = AngularBisector(NER31', NE30, C)
K' = Mirror(K, t)
Ortslinie3 = Locus(K', K)
bragg: 2 * d * sin(β) / λ
f_1 = Function(-f(x), 0, 6 * d)
a_1 = AngularBisector(NER2, NE0, NER1'_1)
L = Point(f_1)
L' = Mirror(L, a_1)
Ortslinie4 = Locus(L', L)
g_1 = Function(-f(x + s1) - d, 0, 6 * d + s1)
h_1 = Function(-f(x + s2) - 2 * d, 0, 6 * d + s2)
M = Point(i)
b_1 = OrthogonalLine(M, i)
c_1 = OrthogonalLine(NE20, b_1)
d_1 = OrthogonalLine(NE30, b_1)
e_1 = OrthogonalLine(NE40, b_1)
i_1 = OrthogonalLine(NE50, b_1)
N = Intersect(b_1, c_1)
O = Intersect(b_1, d_1)
P = Intersect(b_1, e_1)
Q = Intersect(b_1, i_1)
j_1 = AngularBisector(N, NE20, NER21)
R = Point(g_1)
R' = Mirror(R, j_1)
Ortslinie5 = Locus(R', R)
k_1 = AngularBisector(NER35, NE30, O)
S = Point(h_1)
S' = Mirror(S, k_1)
Ortslinie6 = Locus(S', S)
l_1 = Ray(NE20, B)
m_1 = Ray(NE30, C)
n_1 = Ray(NE40, D)
q_3 = Ray(NE50, E)
r_1 = Ray(NE20, N)
s_1 = Ray(NE30, O)
t_1 = Ray(NE40, P)
a_2 = Ray(NE50, Q)
b_2 = Segment(NE0, M)
c_2 = Segment(NE20, N)
d_2 = Segment(NE30, O)
e_2 = Segment(NE40, P)
pl1: b_2 / λ - Div[b_2, λ]
pl2: (c_2 + s1) / λ - Div[c_2 + s1, λ]
pl3: (d_2 + s2) / λ - Div[d_2 + s2, λ]
p1: (pl1 * 360)°
p2: (pl2 * 360)°
p3: (pl3 * 360)°
f_2 = Circle(M, amp)
g_2 = Circle(N, amp)
h_2 = Circle(O, amp)
T, U = Intersect(f_2, i)
V, W = Intersect(g_2, r_1)
Z, A_1 = Intersect(h_2, s_1)
U' = Rotate(U, p1, M)
δ = Angle(U, M, U')
W' = Rotate(W, p2, N)
ε = Angle(W, N, W')
B_1 = Rotate(A_1, p3, O)
ζ = Angle(A_1, O, B_1)
u = Vector(M, U')
v = Vector(N, W')
w = Vector(O, B_1)
C_1 = (16.03750867643542, 7.782165901402618)
D_1 = Translate(C_1, u)
z = Vector(C_1, D_1)
E_1 = Translate(D_1, v)
u_1 = Vector(D_1, E_1)
F_1 = Translate(E_1, w)
v_1 = Vector(E_1, F_1)
w_1 = Vector(C_1, F_1)
G_1 = Point(q)
H_1 = Mirror(G_1, yAxis)
i_2 = Line(H_1, NE0)
j_2 = Line(NER5', NER2)
k_2 = OrthogonalLine(NE0, j_2)
I_1 = Intersect(a_2, i_2)
J_1 = Intersect(t_1, e_2)
K_1 = Intersect(i_2, s_1)
L_1 = Intersect(i_2, r_1)
l_2 = Segment(NE20, L_1)
m_2 = Segment(NE30, K_1)
M_1 = Intersect(t_1, e_2)
N_1 = Intersect(t_1, e_2)
O_1 = Intersect(i_2, t_1)
n_2 = Segment(NE40, O_1)
p_2 = Segment(NE50, I_1)
SF = (3.3317733134907694, 6.647725243996842)
Text1: "(2·d·sin(β))/λ=" + bragg + ""
q_1 = Function(-f_1(x) + y(SF), x(SF), 4 * d + x(SF))
z_1 = Vector(C_1, D_1)
u_2 = Vector(C_1, E_1)
r_2 = Circle(P, amp)
s_2 = Circle(Q, amp)
P_1, Q_1 = Intersect(r_2, t_1)
R_1, S_1 = Intersect(s_2, a_2)
t_2 = Segment(NE50, Q)
pl4: (e_2 + s3) / λ - Div[e_2 + s3, λ]
p4: (pl4 * 360)°
T_1 = Rotate(Q_1, p4, P)
α = Angle(Q_1, P, T_1)
v_2 = Vector(P, T_1)
pl5: (t_2 + s4) / λ - Div[t_2 + s4, λ]
p5: (pl5 * 360)°
U_1 = Rotate(S_1, pl5, Q)
η = Angle(S_1, Q, U_1)
w_2 = Vector(Q, U_1)
V_1 = Translate(F_1, v_2)
z_2 = Vector(F_1, V_1)
W_1 = Translate(V_1, w_2)
u_3 = Vector(V_1, W_1)
v_3 = Vector(C_1, V_1)
z_3 = Vector(C_1, W_1)
a_3 = Segment(NE0, NE20)
θ = Angle(F, NE0, NE20)
b_3 = Segment(F, NE20)
q_2 = Function(-f_1(x) - g_1(x + l_2) - d + y(SF), x(SF), 4 * d + x(SF))
p_1 = Function(-f_1(x) - g_1(x + l_2) - h_1(x + m_2) - 3 * d + y(SF), x(SF), 4 * d + x(SF))