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  1. Delivered before the Optical Society of London, Feb. 10, 1927;published in the Trans. of the Optical Society,  28, pp. 225–284; 1926–7.
    [CrossRef]
  2. James P. C. Southall, Conjugate surfaces of a spherical refracting surface. J.O.S.A. & R.S.I.,  16, pp. 380–397, 1928.
    [CrossRef]
  3. See J. P. C. Southall, loc. cit., p. 384.
  4. F. Lippich, Über Brechung und Reflexion unendlich dünner Strahlensysteme an Kugelflächen. Denkschriften der kaiserl. Akad. der Wissenschaften zu Wien,  38, pp. 163–192; 1878.

1928 (1)

James P. C. Southall, Conjugate surfaces of a spherical refracting surface. J.O.S.A. & R.S.I.,  16, pp. 380–397, 1928.
[CrossRef]

1878 (1)

F. Lippich, Über Brechung und Reflexion unendlich dünner Strahlensysteme an Kugelflächen. Denkschriften der kaiserl. Akad. der Wissenschaften zu Wien,  38, pp. 163–192; 1878.

Lippich, F.

F. Lippich, Über Brechung und Reflexion unendlich dünner Strahlensysteme an Kugelflächen. Denkschriften der kaiserl. Akad. der Wissenschaften zu Wien,  38, pp. 163–192; 1878.

Southall, J. P. C.

See J. P. C. Southall, loc. cit., p. 384.

Southall, James P. C.

James P. C. Southall, Conjugate surfaces of a spherical refracting surface. J.O.S.A. & R.S.I.,  16, pp. 380–397, 1928.
[CrossRef]

J.O.S.A. & R.S.I. (1)

James P. C. Southall, Conjugate surfaces of a spherical refracting surface. J.O.S.A. & R.S.I.,  16, pp. 380–397, 1928.
[CrossRef]

loc. cit. (1)

See J. P. C. Southall, loc. cit., p. 384.

Über Brechung und Reflexion unendlich dünner Strahlensysteme an Kugelflächen. Denkschriften der kaiserl. Akad. der Wissenschaften zu Wien (1)

F. Lippich, Über Brechung und Reflexion unendlich dünner Strahlensysteme an Kugelflächen. Denkschriften der kaiserl. Akad. der Wissenschaften zu Wien,  38, pp. 163–192; 1878.

Other (1)

Delivered before the Optical Society of London, Feb. 10, 1927;published in the Trans. of the Optical Society,  28, pp. 225–284; 1926–7.
[CrossRef]

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Figures (5)

F. 1
F. 1

Diagram of a crescent-shaped meniscus lens with the centres of curvature of the two surfaces at C1, C2 and vertices at A1, A2. A straight line drawn through the centre C1 of the first surface of the lens meets this surface at B; the opposite extremity of the diameter BE being the point marked E. The radius C2D of the second surface is drawn parallel to C1B. The optical centre of the lens (which is one of the two centres of similitude of the pair of circles whose arcs are A1B and A2D) is M where the straight line BD crosses the optical axis C1C2. The other centre of similitude is at N where the straight line DE crosses the optical axis. The dotted circle described on MN as diameter is the section of the harmonic sphere.

F. 2
F. 2

Lens surrounded by same medium on both sides showing path RB1B2T of the chief ray of a narrow bundle of rays. The position of the focal points F1 F1′ for the first refraction, F2, F2′ for the second refraction, and F, F′ for the lens as a whole are indicated; and also the positions of a pair of conjugate points P, P′. All these points are shown for the imagery in the sagittal sections corresponding to the three portions of the path of the chief ray.

F. 3
F. 3

Auxiliary diagram for construction of first focal point F, first unit point U, and first focal length f = FU.

F. 4
F. 4

Auxiliary diagram for construction of second focal point F′, second unit point U′, and second focal length f′ = F′U′.

F. 5
F. 5

First surface of lens, showing ray incident on it, and construction of point P corresponding to a given value of the magnification-ratio m.

Equations (18)

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C 1 M C 2 M = C 1 N NC 2 = A 1 C 1 A 2 C 2 = r 1 r 2 ;
A 1 M = r 1 d r 1 r 2 , A 1 N = ( 2 r 2 + d ) r 1 r 1 + r 2 ,
f 1 = F 1 B 1 , f 1 = F 1 B 1 ; f 2 = F 2 B 2 , f 2 = F 2 B 2 .
f 1 f 1 = f 2 f 2 = n n ,
D 1 = n f 1 = n f 1 , D 2 = n f 2 = n f 2 .
D = D 1 + D 2 t · D 1 · D 2 ,
t = B 1 B 2 n .
n x · D = x · D n = m ,
FU = U F = n D ;
f = f = n D , or D = n f = n f ,
B 1 U n = D 2 D t , B 2 U n = D 1 D t ; B 1 F n = 1 t · D 2 D , B 2 F n = 1 t · D 1 D .
FP = f m ,
m = m 1 · m 2 ;
m 1 = m · D D 1 + m · D 2 .
m 1 = F 1 F 2 F 1 B 1 F 2 B 2 m .
a = 1 m 1 m 1 · n 2 n 2 n 2 · r 1 , k = n n a .
B 1 P B 1 S = a r 1 ;
a r 1 = 1 m 1 m 1 · n 2 n 2 n 2