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References

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  1. Herzberger, Physica 2, 239 (1935).
    [CrossRef]

1935 (1)

Herzberger, Physica 2, 239 (1935).
[CrossRef]

Herzberger,

Herzberger, Physica 2, 239 (1935).
[CrossRef]

Physica (1)

Herzberger, Physica 2, 239 (1935).
[CrossRef]

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Figures (12)

F. 1
F. 1

Refraction at a single surface a ( U 1 V ) o unit vector normal to the surface s , s unit vectors along the ray before and after refraction.

F. 2
F. 2

Shifting of a line element along two neighboring rays from A to B.

F. 3
F. 3

Three neighboring rays in arbitrary situation in object and image space.

F. 4
F. 4

The determining elements of a meridian ray in Gaussian optics. Ō, O′ origin of coordinates.

F. 5
F. 5

Two rays through the same point of the axis.

F. 6
F. 6

Definition of the apparent distance of the object and image origin , respectively, g′.

F. 7
F. 7

Two rays, one entering parallel to the axis, the other sorting parallel to the axis. Figure to demonstrate the equation given by Gauss between the focal lengths.

F. 8
F. 8

Two rays, one sorting at the object origin. The other converging to the image origin. Figure to demonstrate the formula of Huygens.

F. 9
F. 9

Two rays, one leaving the system parallel to the axis, the other coming from the image origin. Origin on object side in the focal point.

F. 10
F. 10

The image of a finite line element orthogonal to the axis.

F. 11
F. 11

The image of a line element orthogonal to the axis at the focal point.

F. 12
F. 12

The image of an infinite line element in afocal systems.

Equations (96)

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n s × o = n s × o .
( n s n s ) × o = 0 ,
( n s n s ) = Γ o .
Γ = n cos n cos ,
o · a u = o · a υ = 0 .
o υ a u = o u a υ = o a u υ .
n s u a υ n s u a υ = o u a υ , n s υ a u n s υ a u = o υ a u .
n ( s u a υ s υ a u ) = n ( s u a υ s υ a u ) = I .
b = a + λ s ,
b u = a u + λ u s + λ s u , b υ = a υ + λ υ s + λ s υ .
n ( b u s υ b υ s u ) = n ( a u s υ a υ s u ) .
I = n ( s u a υ s υ a u ) = n ( s u a υ s υ a u )
n u a υ n υ a u = n u a υ n υ a u .
( 1 ) n by a a by n or ( 2 ) n by a , a by n , ( 3 ) n by a , a by n , n by a , a by n .
n ( d 1 s d 2 a d 2 s d 1 a ) = n ( d 1 s d 2 a d 2 s d 1 a ) ,
n ( d s d a 1 d s 1 d a ) = n ( d s d a 1 d s 1 d a )
n ( h 1 σ h σ 1 ) = n ( h ¯ 1 σ h ¯ σ 1 ) .
( 1 ) n σ h ¯ , h ¯ n σ , ( 2 ) n σ h , h n σ , ( 3 ) n σ h ¯ , n σ h , h ¯ n σ , h n σ .
σ 1 : h 1 = σ : h .
σ 1 : h 1 = σ : h .
h / h ¯ = δ , σ / σ = γ .
h / σ = , h ¯ / σ = g .
= γ z , z = g δ , g γ = z ¯ , z ¯ = / δ ,
= γ δ g .
σ 1 = 0 , σ 2 = 0 .
n h 1 σ 2 = n h ¯ 2 σ 1 .
n h 1 / σ 1 = n h ¯ 2 / σ 2 or n f ¯ = n f .
h ¯ 1 = h 2 = 0 .
n h 1 σ 2 = n h ¯ 2 σ 1 .
n σ 2 / h ¯ 2 = n σ 1 / h 1
n / g 0 = n / 0
σ 1 = σ 2 .
h ¯ 1 = 0 , σ 2 = 0 .
n h 2 σ 1 = n h 2 σ 1
( n h 2 / n h 2 ) σ 1 / σ 1 = 1
( n / n ) δ γ 0 = 1 .
δ = f ¯ / z ¯ ,
( n f ¯ / n z ¯ ) γ 0 = 1 = γ 0 f / z ¯ .
z ¯ = f γ 0 .
z ¯ = f
σ 1 = 0 , h 2 = 0 ,
n h 1 σ 2 = n h 1 σ 2 ,
( n / n ) δ γ 0 = 1 .
δ = z / f ,
γ 0 = n f / n z = f ¯ / z .
z = f ¯
h 1 = h 1 = 0 .
n h σ 1 = n h σ 1 ,
σ 1 / σ 1 = γ 0 = γ 0 = γ 1
( n / n ) δ γ 1 = 1 .
δ = n / n γ 1 = β
β = z / f = f ¯ / z ¯ .
z ¯ = f ¯ and z = f ,
h ¯ 1 = σ 1 = 0
n h 1 σ = n h ¯ σ 1
h ¯ / σ = n h 1 / n σ 1 .
g = n f ¯ / n = f .
h / σ = = n f / n = f ¯ .
σ 1 = σ 1 = 0 .
n σ h 1 = n σ h 1
( n / n ) γ δ 1 = 1 , δ 1 = δ = δ .
n B Γ = n .
n ( σ 1 h σ h 1 ) = n ( σ 1 h ¯ σ h ¯ 1 ) .
n ( 1 / z 1 / z 1 ) = n δ δ 1 ( 1 / z 1 / z 1 ) ,
n g ( 1 z ¯ 1 / z ¯ ) = n 1 ( z / z 1 1 ) ,
n g 1 ( z ¯ / z ¯ 1 1 ) = n ( 1 z 1 / z )
n ( z ¯ 1 z ¯ ) = n γ γ 1 ( z z 1 ) .
( n / z ) β 0 2 n / z = ( n / z 1 ) β 2 n / z 1 ,
( n / z ) β 0 2 n / z = n / f β 0 = ( n / f ¯ ) β 0 .
n / z n / z = n / f = n / f .
1 / n z 1 / n z = 1 / n f = 1 / n f .
= 1 = f ¯ , g = g 1 = f ,
z ¯ z = z ¯ 1 z 1 .
z ¯ z = f ¯ f
z = z 1 = Γ
n Γ 2 z n z ¯ = n Γ 1 2 z n z ¯ 1 .
n Γ 2 z = n z .
h = κ h ¯ + λ n σ , n σ = μ h ¯ + ν n σ .
( h 1 n σ 2 h 2 n σ 1 ) = ( κ ν λ μ ) ( h ¯ 1 n σ 2 h ¯ 2 n σ 1 ) .
κ ν λ μ = 1 .
κ = δ , λ = 0 / n , μ = n / f , ν = n γ 0 / n .
( n / n ) β 0 γ = 1 ,
κ = β 0 = 1 , ν = n γ / n = 1 , λ = 0 .
κ = β 0 = n / n , ν = n γ / n = n / n , λ = 0 .
κ = ν = 0 , λ = f ¯ / n , μ = n / f ,
f ¯ / n = f / n .
μ = 0 , κ = β , ν = ( n / n ) Γ .
( n / n ) β Γ = 1 .
h = h , n σ = μ h + n σ .
μ = ( n n ) / r .
h = h , n σ = ( ( n n ) / r ) h + n σ .
h = h ¯ + ( d / n ) n σ , n σ = n σ .
( 1 0 ( n n ) / r 1 ) = R ( r ) .
( 1 d / n 0 1 ) = D ( d ) .
( h n σ ) = R ( r ) ( h ¯ n σ ) , resp . ( 68 ) : ( h n σ ) = D ( d ) ( h ¯ n σ ) .
( h n σ ) = D ( s ) R ( τ κ ) D ( d κ , κ 1 ) R ( r κ 1 ) R ( r 1 ) D ( s ) ( h ¯ n σ ) .