Lichtbrechung an mehreren Prismen
Author: Günter vom Stein

Lösung zeigen

In roter Farbe:
Jeweiliger Winkel an der 
(abgeschnittenen) 
Spitze des Prismas

Winkel im Prisma zeigen

Breite der Prismen

Brechzahl der Glassorte

Verändere die Breite und die Brechzahl.
Notiere Deine Beobachtung.
Schiebe ggf. die Zeichenebene nach links, um 
den/die Schnittpunkt(e) zu untersuchen.
 

Sage voraus, wie sich die Brechungen
der vier Lichtstrahlen beim Durchgang 
durch die vier verschiedenen Prismen 
unterscheiden.

Lichtstrahlen Start

B_1 = (0, 4)
s = OrthogonalLine(B_1, yAxis)
n = 1.44 (slider from 1 to 1.6, step 0.01)
b = 1.71 (slider from 0 to 2.5, step 0.01)
M = Point(yAxis)
G = Point(yAxis)
e = OrthogonalLine(G, yAxis)
F = Point(yAxis)
f = OrthogonalLine(F, yAxis)
E = Point(yAxis)
h = OrthogonalLine(E, yAxis)
D = Point(yAxis)
g = OrthogonalLine(D, yAxis)
A = Intersect(xAxis, yAxis)
c = Circle(A, b)
B, C = Intersect(c, xAxis)
b_4 = OrthogonalLine(C, xAxis)
L = Intersect(b_4, h)
J = Intersect(b_4, g)
q = Circle(M, J, L)
Z, A_1 = Intersect(q, f)
V, W = Intersect(q, e)
a = OrthogonalLine(B, xAxis)
I = Intersect(a, g)
H = Intersect(a, h)
p = Circle(M, I, H)
R, S = Intersect(p, f)
P, Q = Intersect(p, e)
Vieleck3, r_2, a_2, w, p_1 = Polygon(R, A_1, W, P)
C_1 = Intersect(p_1, s)
t = OrthogonalLine(C_1, p_1)
V_1 = Intersect(t, yAxis)
K = Point(yAxis)
d = OrthogonalLine(K, yAxis)
Vieleck1, h_1, l, j, i = Polygon(H, L, J, I)
k = OrthogonalLine(M, yAxis)
N, O = Intersect(p, d)
T, U = Intersect(q, d)
Vieleck2, i_1, j_1, a_1, r_1 = Polygon(I, J, A_1, R)
Vieleck4, p_2, w_1, u, n_2 = Polygon(P, W, U, N)
Vieleck5, m, n_1, u_1 = Polygon(N, U, M)
D_1 = Rotate(V_1, -asin(sin(Angle[t, s]) / n), C_1)
b_1 = Ray(C_1, D_1)
E_1 = Intersect(a_2, b_1)
F_1 = Point(xAxis)
c_1 = OrthogonalLine(F_1, xAxis)
G_1 = Intersect(s, c_1)
d_1 = Ray(C_1, G_1)
H_1 = Point(yAxis)
e_1 = OrthogonalLine(H_1, yAxis)
I_1 = Intersect(e_1, n_2)
f_1 = OrthogonalLine(I_1, n_2)
J_1 = Rotate(H_1, -asin(sin(Angle[f_1, e_1]) / n), I_1)
g_1 = Ray(I_1, J_1)
K_1 = Intersect(c_1, e_1)
k_1 = Ray(I_1, K_1)
m_1 = OrthogonalLine(E_1, a_2)
s_1 = Segment(C_1, E_1)
N_1 = Point(m_1)
O_1 = Rotate(N_1, asin(sin(Angle[s_1, m_1]) * n), E_1)
b_2 = Ray(E_1, O_1)
Q_1 = Point(yAxis)
R_1 = Point(yAxis)
c_2 = OrthogonalLine(Q_1, yAxis)
d_2 = OrthogonalLine(R_1, yAxis)
S_1 = Intersect(u_1, d_2)
T_1 = Intersect(r_1, c_2)
e_2 = OrthogonalLine(S_1, u_1)
f_2 = OrthogonalLine(T_1, r_1)
L_1 = Intersect(f_1, yAxis)
P_1 = Rotate(L_1, -asin(sin(Angle[f_1, k_1]) / n), I_1)
l_1 = Ray(I_1, P_1)
M_1 = Intersect(l_1, w_1)
q_1 = Segment(I_1, M_1)
t_1 = OrthogonalLine(M_1, w_1)
W_1 = Point(t_1)
Z_1 = Rotate(W_1, asin(sin(Angle[q_1, t_1]) * n), M_1)
i_2 = Ray(M_1, Z_1)
U_1 = Intersect(f_2, yAxis)
A_2 = Intersect(c_2, c_1)
B_2 = Rotate(U_1, -asin(sin(Angle[f_2, c_2]) / n), T_1)
l_2 = Ray(T_1, B_2)
C_2 = Intersect(l_2, j_1)
m_2 = Segment(T_1, C_2)
q_2 = OrthogonalLine(C_2, j_1)
s_2 = Ray(T_1, A_2)
D_2 = Point(q_2)
E_2 = Rotate(D_2, asin(sin(Angle[m_2, q_2]) * n), C_2)
g_2 = Ray(C_2, E_2)
F_2 = Intersect(e_2, yAxis)
G_2 = Rotate(F_2, -asin(sin(Angle[e_2, d_2]) / n), S_1)
h_2 = Ray(S_1, G_2)
H_2 = Intersect(h_2, n_1)
j_2 = Segment(S_1, H_2)
I_2 = Intersect(c_1, d_2)
k_2 = Ray(S_1, I_2)
t_2 = OrthogonalLine(H_2, n_1)
J_2 = Point(t_2)
K_2 = Rotate(J_2, asin(sin(Angle[j_2, t_2]) * n), H_2)
a_3 = Ray(H_2, K_2)
L_2 = Intersect(c_1, xAxis)
b_3 = OrthogonalLine(L_2, c_1)
N'_1 = Mirror(N, b_3)
U'_1 = Mirror(U, b_3)
M' = Mirror(M, b_3)
Vieleck5', m', n', u' = Polygon(N'_1, U'_1, M')
I' = Mirror(I, b_3)
J' = Mirror(J, b_3)
M_2 = Mirror(A_1, b_3)
R'_1 = Mirror(R, b_3)
Vieleck2', i', j', m_3, r' = Polygon(I', J', M_2, R'_1)
R' = Mirror(R, b_3)
N_2 = Mirror(A_1, b_3)
W'_1 = Mirror(W, b_3)
P'_1 = Mirror(P, b_3)
Vieleck3', r'_1, n_3, w', p' = Polygon(R', N_2, W'_1, P'_1)
P' = Mirror(P, b_3)
W' = Mirror(W, b_3)
U' = Mirror(U, b_3)
N' = Mirror(N, b_3)
Vieleck4', p'_1, w'_1, u'_1, n'_1 = Polygon(P', W', U', N')
O_2 = Mirror(S_1, b_3)
P_2 = Mirror(I_2, b_3)
c_3 = Ray(O_2, P_2)
Q_2 = Mirror(I_1, b_3)
R_2 = Mirror(K_1, b_3)
d_3 = Ray(Q_2, R_2)
S_2 = Mirror(C_1, b_3)
T_2 = Mirror(G_1, b_3)
e_3 = Ray(S_2, T_2)
U_2 = Mirror(T_1, b_3)
V_2 = Mirror(A_2, b_3)
f_3 = Ray(U_2, V_2)
W_2 = Mirror(S_1, b_3)
Z_2 = Mirror(H_2, b_3)
g_3 = Segment(W_2, Z_2)
A_3 = Mirror(I_1, b_3)
B_3 = Mirror(M_1, b_3)
h_3 = Segment(A_3, B_3)
C_3 = Mirror(C_1, b_3)
D_3 = Mirror(E_1, b_3)
i_3 = Segment(C_3, D_3)
E_3 = Mirror(T_1, b_3)
F_3 = Mirror(C_2, b_3)
j_3 = Segment(E_3, F_3)
G_3 = Mirror(H_2, b_3)
H_3 = Mirror(K_2, b_3)
k_3 = Ray(G_3, H_3)
I_3 = Mirror(M_1, b_3)
J_3 = Mirror(Z_1, b_3)
l_3 = Ray(I_3, J_3)
K_3 = Mirror(E_1, b_3)
L_3 = Mirror(O_1, b_3)
p_3 = Ray(K_3, L_3)
M_3 = Mirror(C_2, b_3)
N_3 = Mirror(E_2, b_3)
q_3 = Ray(M_3, N_3)
O_3 = (1.883503142894795, 6.089793963068175)
P_3 = Mirror(O_3, j_2)
Q_3 = Mirror(S_1, b_3)
R_3 = Mirror(H_2, b_3)
r_3 = Segment(Q_3, R_3)
o = true
α = Angle(J, I, R)
β = Angle(A_1, J, I)
γ = Angle(A_1, R, P)
δ = Angle(W, A_1, R)
ε = Angle(W, P, N)
ζ = Angle(U, W, P)
η = Angle(N, M, U)
Text2: "" + (180° - 2 * ε)
Text3: "" + (180° - 2 * γ)
Text4: "" + (180° - 2 * α)
v = false
r = true