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  1. Huygens’Œuvres complétes, 13, p. 63.—See also Southall’sMirrors, Prisms and Lenses, revised ed., p. 617, New York, 1923.
  2. A course of lectures on Natural Philosophy and the Mechanical Arts, by Young Thomas, London, 1807, in two volumes. See 2, Art. 425, p. 73.
  3. Thomas Young, On the mechanism of the human eye, Phil. Trans.,  92, p. 23; 1801.
    [CrossRef]
  4. See, for example, A. Gullstrand, Appendix I of Vol. I of English Translation of Helmholtz’sPhysiological Optics (published by the Optical Society of America, 1924), pp. 272–277.—Also, Southall’sPrinciples and Methods of Geometrical Optics, 2nd ed. (New York, 1913), Appendix to Chapter XI;and Southall’sMirrors, Prisms and Lenses, revised ed., New York, 1923, pp. 529–532.
  5. E. v. Högh, Dioptrische Untersuchungen. C. P. Goerz Festschrift (Berlin-Friedenau, 1911), pp. 171–175.—See also Southall’sPrinciples and Methods of Geometrical Optics, second ed., Appendix to chap. XI, page 366a, New York, 1913.

1801 (1)

Thomas Young, On the mechanism of the human eye, Phil. Trans.,  92, p. 23; 1801.
[CrossRef]

Gullstrand, A.

See, for example, A. Gullstrand, Appendix I of Vol. I of English Translation of Helmholtz’sPhysiological Optics (published by the Optical Society of America, 1924), pp. 272–277.—Also, Southall’sPrinciples and Methods of Geometrical Optics, 2nd ed. (New York, 1913), Appendix to Chapter XI;and Southall’sMirrors, Prisms and Lenses, revised ed., New York, 1923, pp. 529–532.

Helmholtz’s,

See, for example, A. Gullstrand, Appendix I of Vol. I of English Translation of Helmholtz’sPhysiological Optics (published by the Optical Society of America, 1924), pp. 272–277.—Also, Southall’sPrinciples and Methods of Geometrical Optics, 2nd ed. (New York, 1913), Appendix to Chapter XI;and Southall’sMirrors, Prisms and Lenses, revised ed., New York, 1923, pp. 529–532.

Högh, E. v.

E. v. Högh, Dioptrische Untersuchungen. C. P. Goerz Festschrift (Berlin-Friedenau, 1911), pp. 171–175.—See also Southall’sPrinciples and Methods of Geometrical Optics, second ed., Appendix to chap. XI, page 366a, New York, 1913.

Huygens’,

Huygens’Œuvres complétes, 13, p. 63.—See also Southall’sMirrors, Prisms and Lenses, revised ed., p. 617, New York, 1923.

Thomas, Young

A course of lectures on Natural Philosophy and the Mechanical Arts, by Young Thomas, London, 1807, in two volumes. See 2, Art. 425, p. 73.

Young, Thomas

Thomas Young, On the mechanism of the human eye, Phil. Trans.,  92, p. 23; 1801.
[CrossRef]

Phil. Trans. (1)

Thomas Young, On the mechanism of the human eye, Phil. Trans.,  92, p. 23; 1801.
[CrossRef]

Other (4)

See, for example, A. Gullstrand, Appendix I of Vol. I of English Translation of Helmholtz’sPhysiological Optics (published by the Optical Society of America, 1924), pp. 272–277.—Also, Southall’sPrinciples and Methods of Geometrical Optics, 2nd ed. (New York, 1913), Appendix to Chapter XI;and Southall’sMirrors, Prisms and Lenses, revised ed., New York, 1923, pp. 529–532.

E. v. Högh, Dioptrische Untersuchungen. C. P. Goerz Festschrift (Berlin-Friedenau, 1911), pp. 171–175.—See also Southall’sPrinciples and Methods of Geometrical Optics, second ed., Appendix to chap. XI, page 366a, New York, 1913.

Huygens’Œuvres complétes, 13, p. 63.—See also Southall’sMirrors, Prisms and Lenses, revised ed., p. 617, New York, 1923.

A course of lectures on Natural Philosophy and the Mechanical Arts, by Young Thomas, London, 1807, in two volumes. See 2, Art. 425, p. 73.

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Figures (8)

Fig. 1
Fig. 1

Young’s construction of ray refracted at a spherical surface. Straight lines BS, BS′ show path of ray before and after refraction. Points C and K are centers of perspective of two ranges of conjugate points on this ray.

Fig. 2
Fig. 2

P, Q, R, S and P′, Q′, R′, S′ are two perspective ranges of points with respect to point E as center of perspective.

Fig. 3
Fig. 3

Conjugate spheres for a fixed point of incidence and for a given value of the magnificaion-ratio m. The centers of these spheres are at Z and Z′ and their radii are ZP and Z′P′. The effective zones are UPV and U′P′V′.

Fig. 4
Fig. 4

Conjugate spheres for a fixed point of incidence and for a given value of the magnification-ratio m. The centers of these spheres are at Z and Z′ and their radii are ZP and Z′P′. The effective zones are UPV and U′P′V′.

Fig. 5
Fig. 5

Focal point sphere for magnification-ratio m=0.

Fig. 6
Fig. 6

Focal point sphere for magnification-ratio m = ∞.

Fig. 7
Fig. 7

Conjugate spheres for magnification-ratio m = −1.

Fig. 8
Fig. 8

Chief incident ray crosses optical axis at L and meets spherical refracting surface at B and concentric surface σ at S. PZ is parallel to CS, and CY is perpendicular to BS.

Equations (30)

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n sin α = n sin α ,
CK = n n r sin 2 α .
m = P V PV .
Q = n q , Q = n q ,
β 2 Q = Q + β D , β m Q = Q ,
Sagittal Section : D = n cos α n cos α r , β = 1 . Meridian Section : D = n cos α n cos α r cos α cos α , β = cos α cos α .
Q = Q + D , m Q = Q ,
( 1 m m ) 2 Q 2 + 1 m m 2 n r Q cos α n 2 n 2 r 2 = 0 .
a = 1 m m n 2 n 2 n 2 r , k = n n a ,
q 2 + a 2 2 a q cos α = k 2 ,
q 2 + a 2 2 a q cos α = k 2 ,
a = ( 1 m ) n 2 n 2 n 2 r = n 2 n 2 m a , k = n n a = m k .
CZ = n 2 mn 2 m ( n 2 n 2 ) r ;
C Z = m · CZ = n 2 mn 2 n 2 n 2 r .
C P CP = C M CB = CB CM = m .
CM = r m , CM = m · r ,
ZP MZ = BZ ZP = sin α sin α = n n .
a = 1 m m · n 2 n 2 n 2 · r , k = n n a ,
a = n 2 n 2 n 2 r , k = n n n 2 n 2 r , ( m = 0 ) ,
a = n 2 n 2 n 2 r , k = n n n 2 n 2 r , ( m = ) .
CM = C M = r , C Z = ZC = n 2 + n 2 n 2 n 2 r , k = k = 2 n n n 2 n 2 r , ( m = 1 ) .
α θ = α θ = ϕ .
c sin θ = r sin α .
q 2 2 a q cos α + α 2 k 2 = 0 ;
q = a r ( r 2 c 2 sin 2 θ + 1 n n 2 r 2 n 2 c 2 sin 2 θ ) .
q = n 2 n 2 n 2 ( r 2 c 2 sin 2 θ + n 2 r 2 / n 2 c 2 sin 2 θ ) , ( m = ) ;
BP BS = BZ BC ;
q = a r s .
BY = r 2 c 2 sin 2 θ , YS = n 2 r 2 / n 2 c 2 sin 2 θ .
s = r 2 c 2 sin 2 θ + n 2 r 2 / n 2 c 2 sin 2 θ ;