Bildentstehung und Vergrößerung beim Fernrohr
Author: Günter vom Stein

Strahl(en) von der Spitze eines
weit entfernten Gegenstandes

Bild ohne 
Fernrohr

Bild mit 
Fernrohr

Okular = Lupe

Merksatz einblenden

Gegenstandsgröße

Fernrohr einblenden

Das Auge ist im Vergleich 
zum 'wahren' Auge zu 
groß gezeichnet.

Objektiv

Bild in der Brennebene
des Objektivs

f (Objektiv) = 20 cm

f (Okular) = 5 cm

Vergrößerung = $ \frac{Brennweite \; Objektiv }{Brennweite\; Okular }$   =  $ \frac{ 20 }{5 }  = 4

Brennweite des Auges = 22 mm

(hier zu groß gezeichnet)

Lichtbündel einblenden

       (Hier nur Mitteilung ohne Herleitung)

G = 17.88 (slider from 12 to 20, step 0.0010)
A = Point(yAxis)
A' = Mirror(A, xAxis)
B = Point(xAxis)
c = CircleArc(B, A', A)
B' = Mirror(B, yAxis)
d = CircleArc(B', A, A')
C = Point(xAxis)
e = CircleArc(C, A', A)
D = (-200, 0)
E: (-200, G)
u = Vector(D, E)
F_3 = Intersect(yAxis, xAxis)
a = Ray(E, F_3)
G_3 = Intersect(e, a)
b = Segment(E, G_3)
H = Intersect(e, xAxis)
v = Vector(H, G_3)
I = (-5, 0)
J = (-5, 3)
g = OrthogonalLine(I, xAxis)
K = (-5, -3)
F = (-10, 0)
h = CircleArc(F_3, J, K)
k = CircleArc(F, K, J)
N = (-5, 4)
N' = Mirror(N, xAxis)
j = Segment(N, N')
R = Point(k)
S = Point(k)
T = Point(k)
U = Point(k)
V = Point(k)
W = Point(k)
Z = Point(k)
A_1 = Point(k)
B_1 = Point(k)
C_1 = Point(k)
D_1 = Point(h)
E_1 = Point(h)
F_1 = Point(h)
G_1 = Point(h)
H_1 = Point(h)
I_1 = Point(h)
J_1 = Point(h)
K_1 = Point(h)
L_1 = Point(h)
M_1 = Point(h)
N_1 = Point(h)
Vieleck1, k_1, r, s, t, u_1, v_1, w_1, z_1, a_1, b_1, c_1, j_1, d_1, e_1, f_1, g_1, h_1, i_1, j_2, k_2, l_1, m_1, n_1 = Polygon(K, R, S, T, U, V, W, Z, A_1, B_1, C_1, J, D_1, E_1, F_1, G_1, H_1, I_1, J_1, K_1, L_1, M_1, N_1)
O_1 = Point(c)
P_1 = Point(c)
Q_1 = Point(c)
R_1 = Point(c)
S_1 = Point(c)
T_1 = Point(c)
U_1 = Point(c)
V_1 = Point(c)
W_1 = Point(c)
Z_1 = Point(c)
A_2 = Point(c)
B_2 = Point(c)
C_2 = Point(c)
D_2 = Point(d)
E_2 = Point(d)
F_2 = Point(d)
G_2 = Point(d)
H_2 = Point(d)
I_2 = Point(d)
J_2 = Point(d)
K_2 = Point(d)
L_2 = Point(d)
M_2 = Point(d)
N_2 = Point(d)
O_2 = Point(d)
P_2 = Point(d)
Vieleck2, a', o_1, p_1, q_1, r_1, s_1, t_1, u_2, v_2, w_2, z_2, a_2, b_2, c_2, d_2, e_2, f_2, g_2, h_2, i_2, j_3, k_3, l_2, m_2, n_2, o_2, p_2 = Polygon(A', O_1, P_1, Q_1, R_1, S_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2, M_2, N_2, O_2, P_2)
o = Length(v)
q = false
t_2 = false
M = (-30, 8)
O = (-30, -8)
i = Segment(M, O)
P = Intersect(i, xAxis)
l = OrthogonalLine(F, xAxis)
m = Line(P, b)
Q = Intersect(l, m)
w = Vector(F, Q)
p = Line(Q, xAxis)
T_2 = Intersect(j, p)
a_3 = Ray(T_2, F_3)
U_2 = Intersect(e, a_3)
b_3 = Segment(Q, T_2)
c_3 = Segment(T_2, U_2)
d_3 = Segment(A, A')
V_2 = Intersect(m, j)
n = Ray(V_2, Q)
e_3 = Line(D_1, c_3)
W_2 = Intersect(d_3, e_3)
h_3 = CircleArc(C, H, U_2)
Z_2 = Intersect(e, h_3, 1)
B_3 = Point(h_3)
C_3 = (-30, 6)
D_3 = (-30, -6)
p_3 = CircleArc(F, C_3, D_3)
F' = Mirror(F, i)
E_3 = Mirror(C_3, i)
H_3 = Mirror(D_3, i)
q_3 = Arc(Mirror[Circle[F, C_3], i], E_3, H_3)
I_3 = Point(p_3)
J_3 = Point(p_3)
K_3 = Point(p_3)
L_3 = Point(p_3)
M_3 = Point(p_3)
N_3 = Point(p_3)
O_3 = Point(p_3)
P_3 = Point(p_3)
Q_3 = Point(p_3)
R_3 = Point(p_3)
S_3 = Point(p_3)
T_3 = Point(p_3)
U_3 = Point(p_3)
V_3 = Point(p_3)
W_3 = Point(p_3)
Z_3 = Point(q_3)
A_4 = Point(q_3)
B_4 = Point(q_3)
C_4 = Point(q_3)
D_4 = Point(q_3)
E_4 = Point(q_3)
F_4 = Point(q_3)
G_4 = Point(q_3)
H_4 = Point(q_3)
I_4 = Point(q_3)
J_4 = Point(q_3)
K_4 = Point(q_3)
L_4 = Point(q_3)
M_4 = Point(q_3)
N_4 = Point(q_3)
Vieleck4, g_4, h_4, i_4, j_4, k_4, l_4, m_4, n_4, c_4, i_3, j_5, k_5, l_5, m_3, n_3, o_3, p_4, q_4, r_3, s_3, t_3, u_3, v_3, w_3, d_4, z_3, a_4, b_4, c_5, d_5, e_4, f_4 = Polygon(G_4, H_4, I_4, J_4, K_4, L_4, M_4, N_4, C_3, I_3, J_3, K_3, L_3, M_3, N_3, O_3, P_3, Q_3, R_3, S_3, T_3, U_3, V_3, W_3, D_3, Z_3, A_4, B_4, C_4, D_4, E_4, F_4)
O_4 = (-36.5960325280584, -10.580782771043896)
P_4 = (-36.5960325280584, -13.528743142427295)
Q_4 = (-24.464478551311647, -13.560499425043906)
R_4 = (-24.464478551311647, -10.650077561911118)
Vieleck5, o_4, p_5, q_5, r_4 = Polygon(O_4, P_4, Q_4, R_4)
S_4 = Point(r_4)
T_4 = Point(b)
s_4 = Segment(T_4, S_4)
U_4 = Point(n)
t_4 = Segment(U_4, S_4)
V_4 = (-30, -7)
W_4 = (-10, -7)
Z_4 = (-5, -7)
u_4 = Vector(V_4, W_4)
v_4 = Vector(W_4, V_4)
w_4 = Vector(W_4, Z_4)
z_4 = Vector(Z_4, W_4)
A_5 = (0, -7)
u_5 = Vector(Z_4, A_5)
v_5 = Vector(A_5, Z_4)
B_5 = (-22.997617277700087, -10.86558560104109)
C_5 = (-23.009267619745252, -15.799285473607586)
D_5 = (-0.4534981804661433, -15.799285473607586)
E_5 = (-0.47069253294129487, -10.778866025842179)
Vieleck6, b_5, c_6, d_6, e_5 = Polygon(B_5, C_5, D_5, E_5)
f = Line(V_2, c_3)
L = Intersect(f, d_3)
q_2 = Segment(V_2, L)
r_2 = Segment(L, U_2)
Q_2 = (12, -7)
s_2 = Vector(A_5, Q_2)
f_3 = Vector(Q_2, A_5)
z = Vector(B_3, U_2)
a_5 = Segment(C_3, Q)
g_5 = Ray(D_3, Q)
R_2 = Intersect(g_5, j)
i_5 = Line(R_2, c_3)
S_2 = Intersect(i_5, d_3)
r_5 = Line(K, c_3)
A_3 = Intersect(r_5, d_3)
s_5 = Ray(K, Q)
F_5 = Intersect(s_5, i)
o_5 = false
Vieleck3, e_6, d_7, q_6, f_6 = Polygon(E, D_3, Q, F_5)
Vieleck7, q_7, k_6, a_7, u_6, s_6, r_6 = Polygon(Q, K, A_3, U_2, S_2, R_2)