Die Lupe - ist der Augenabstand von Bedeutung ?
Author: Günter vom Stein

Lupe

Bild

Auge verschieben.

(tatsächliche) Lichtbündel einblenden

Der Fokus-Strahl (Brennpunktstrahl) gibt die
Richtung der Parallelstrahlen hinter der Lupe an

(z.T. theoretischer) Mittel-
punktstrahl der Augenlinse

Das Bild auf
 der Netzhaut
    bleibt stets
 gleich groß.

Die Größenverhältnisse sind nicht realistisch!
Das Auge ist im Vergleich zu groß gezeichnet.
Die Darstellung sagt deshalb nichts über die 
Vergrößerung der Lupe aus.

a = 0 (slider from 0 to 15, step 0.0010)
d_5 = 4.5 (slider from 1 to 5, step 0.1)
D = (-5, 0)
b = OrthogonalLine(D, xAxis)
E = (-5, 1.5)
u = Vector(D, E)
d_1 = Line(E, xAxis)
A = (0, 0)
F = (-5, 0)
F' = (5, 0)
F_1: (0.0, d_5)
G: (0.0, -(d_5))
c = CircleArc(F, G, F_1)
e = CircleArc(F', F_1, G)
a_2 = Line(E, xAxis)
H = Intersect(a_2, yAxis)
f = Segment(E, H)
h = Ray(H, F')
i = Ray(E, A)
I = Intersect(h, i)
j = Ray(G, I)
k = Ray(F_1, I)
l = Segment(E, F_1)
m = Segment(E, G)
E'_1 = Mirror(E, xAxis)
v = Vector(D, E'_1)
H' = Mirror(H, xAxis)
n = Segment(E'_1, H')
p = Ray(H', F')
q = Ray(E'_1, A)
J = Intersect(p, q)
r = OrthogonalLine(F', xAxis)
K: (5.0 + a, 3.0)
L: (2.0 + a, 0.0)
K'_1 = Mirror(K, xAxis)
s = CircleArc(L, K'_1, K)
L'_1 = Mirror(L, r)
K'' = Mirror(K'_1, r)
K'_2 = Mirror(K, r)
o = 120
M: (12.0 + a, 0.0)
N = Intersect(r, i)
O = Intersect(r, q)
j_1 = Line(K'_1, p)
k_1 = Line(K, p)
Z = Intersect(k_1, yAxis)
A_1 = Intersect(j_1, yAxis)
h_1 = OrthogonalLine(J, xAxis)
B_1 = Intersect(h_1, xAxis)
v_1 = Vector(B_1, J)
w_1 = Vector(B_1, I)
s_1 = Line(F_1, G)
B = Point(s_1)
C = Point(s_1)
t_1 = Segment(B, C)
E_1 = Point(c)
G_1 = Point(c)
I_1 = Point(c)
J_1 = Point(c)
K_1 = Point(c)
L_1 = Point(c)
M_1 = Point(c)
N_1 = Point(c)
O_1 = Point(c)
P_1 = Point(c)
Q_1 = Point(c)
R_1 = Point(c)
S_1 = Point(e)
T_1 = Point(e)
U_1 = Point(e)
V_1 = Point(e)
W_1 = Point(e)
Z_1 = Point(e)
A_2 = Point(e)
C_2 = Point(e)
D_2 = Point(e)
E_2 = Point(e)
F_2 = Point(e)
G_2 = Point(e)
H_2 = Point(e)
I_2 = Point(e)
J_2 = Point(c)
K_2 = Point(c)
H_1 = Point(s)
L_2 = Point(s)
N_2 = Point(s)
O_2 = Point(s)
Q_2 = Point(s)
R_2 = Point(s)
S_2 = Point(s)
T_2 = Point(s)
U_2 = Point(s)
L_3 = Point(s)
M_3 = Point(s)
N_3 = Point(s)
O_3 = Point(s)
b_4 = Segment(K, K'_1)
L' = Mirror(L, b_4)
V_2 = Mirror(K'_1, b_4)
K' = Mirror(K, b_4)
s' = Arc(Mirror[Circle[L, K'_1], b_4], V_2, K')
g = CircleArc(M, V_2, K')
P = Intersect(xAxis, b_4)
t = Line(P, h)
Q = Intersect(t_1, t)
R = Intersect(g, t, 1.0)
a_1 = Segment(Q, R)
d = Line(F, F')
b_1 = Segment(E, Q)
c_1 = Line(F_1, h)
S = Intersect(c_1, b_4)
e_1 = Line(V_2, h)
T = Intersect(e_1, t_1)
Vieleck1, e_2, t_2, v_2, r_1, s_2, f_1 = Polygon(E, T, V_2, R, S, F_1)
E' = Mirror(E, d)
T' = Mirror(T, d)
U = Mirror(V_2, d)
R' = Mirror(R, d)
S' = Mirror(S, d)
V = Mirror(F_1, d)
Vieleck1', e', t', u_1, r', s'_1, v_3 = Polygon(E', T', U, R', S', V)
W = Intersect(g, d)
g_1 = CircleArc(M, W, R')
p_1 = CircleArc(M, R, W)
C_1 = Intersect(g, g_1, 1.0)
D_1 = Intersect(g, p_1, 1.0)
B_2 = Intersect(g, p_1, 1.0)
M_2 = Point(g_1)
P_2 = Point(p_1)
w = Vector(M_2, R')
z = Vector(P_2, B_2)
i_1 = false
W_2 = Point(h)
Z_2 = (7.028271009134615, -8.93515045805001)
A_3 = (7.028271009134615, -11.972392752562177)
B_3 = (22.67467070813669, -11.926373929918054)
C_3 = (22.67467070813669, -8.93515045805001)
Vieleck2, z_2, a_3, b_3, c_3 = Polygon(Z_2, A_3, B_3, C_3)
l_1 = Segment(C_3, W_2)
D_3 = Point(a_1)
E_3 = (7.396421590287606, 10.530811520414339)
F_3 = (7.396421590287606, 8.321908033496399)
G_3 = (17.796675507859575, 8.321908033496399)
H_3 = (17.796675507859575, 10.530811520414339)
Vieleck3, e_3, f_3, g_3, h_3 = Polygon(E_3, F_3, G_3, H_3)
m_1 = Segment(D_3, F_3)
I_3 = Point(c)
J_3 = Point(c)
K_3 = Point(c)
P_3 = Point(c)
Q_3 = Point(c)
R_3 = Point(c)
S_3 = Point(c)
T_3 = Point(c)
U_3 = Intersect(c, d, 1.0)
V_3 = Point(c)
W_3 = Point(c)
Z_3 = Point(c)
A_4 = Point(c)
B_4 = Point(c)
C_4 = Point(c)
D_4 = Point(c)
E_4 = Point(c)
F_4 = Point(e)
G_4 = Point(e)
H_4 = Point(e)
I_4 = Point(e)
J_4 = Point(e)
K_4 = Point(e)
L_4 = Point(e)
M_4 = Point(e)
N_4 = Point(e)
O_4 = Point(e)
P_4 = Point(e)
Q_4 = Point(e)
R_4 = Point(e)
S_4 = Point(e)
T_4 = Point(e)
U_4 = Point(e)
Vieleck4, i_3, j_3, k_3, p_3, q_3, r_3, s_3, t_3, u_3, v_4, w_3, z_3, a_4, b_2, c_4, d_4, e_4, f_4, g_4, h_4, i_4, j_4, k_4, l_4, m_4, n_4, o_4, p_4, q_4, r_4, s_4, t_4, u_4 = Polygon(I_3, J_3, K_3, P_3, Q_3, R_3, S_3, T_3, U_3, V_3, W_3, Z_3, A_4, B_4, C_4, D_4, E_4, F_4, G_4, H_4, I_4, J_4, K_4, L_4, M_4, N_4, O_4, P_4, Q_4, R_4, S_4, T_4, U_4)
V_4 = Point(s)
W_4 = Point(s)
Z_4 = Point(s)
A_5 = Point(s)
B_5 = Point(s)
C_5 = Point(s)
D_5 = Point(s)
E_5 = Point(s)
F_5 = Point(s)
G_5 = Point(s)
H_5 = Point(s)
I_5 = Point(s)
J_5 = Point(s)
K_5 = Point(s)
L_5 = Point(s)
M_5 = Point(s)
N_5 = Point(s)
O_5 = Point(s)
P_5 = Point(s)
Q_5 = Point(s)
R_5 = Point(s')
S_5 = Point(s')
T_5 = Point(s')
U_5 = Point(s')
V_5 = Point(s')
W_5 = Point(s')
Z_5 = Point(s')
A_6 = Point(s')
B_6 = Point(s')
C_6 = Point(s')
D_6 = Point(s')
E_6 = Point(s')
F_6 = Point(s')
G_6 = Point(s')
H_6 = Point(s')
I_6 = Point(s')
Vieleck5, v_5, w_4, z_4, a_5, b_5, c_5, d_2, e_5, f_5, g_5, h_5, i_5, j_5, k_5, l_5, m_5, n_5, o_5, p_5, q_5, r_5, s_5, t_5, u_5, v_6, w_5, z_5, a_6, b_6, c_6, d_6, e_6, f_6, g_6, h_6, i_6 = Polygon(V_4, W_4, Z_4, A_5, B_5, C_5, D_5, E_5, F_5, G_5, H_5, I_5, J_5, K_5, L_5, M_5, N_5, O_5, P_5, Q_5, R_5, S_5, T_5, U_5, V_5, W_5, Z_5, A_6, B_6, C_6, D_6, E_6, F_6, G_6, H_6, I_6)