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  1. Œuvres complètes de Christiaan. Huygens publiées par la Société Hollandaise des Sciences. Tome treizième. Dioptrique. La Haye; 1916.
  2. Loc. cit., pp. 40, foll.
  3. Molyneux’s “Dioptrica nova” (1692), pp. 42, 48, 63 and 68. Also article by Halley on “An Instance of the Excellence of the Modern Algebra, in the Resolution of the Problem of finding the Foci of Optick Glasses universally”: Phil. Transactions,  17, pp. 960–969; 1693.
    [CrossRef]
  4. Loc. cit., pp. 198, foll.
  5. See J. O. S. A. & R. S. I.,  6, p. 293, 1922.
    [CrossRef]
  6. Loc. cit., pp. 48, foll.
  7. He makes the same statement again in his “Treatise on Light,” the last chapter of which is devoted to a discussion of the Cartesian ovals and the forms of aplanatic optical surfaces and aplanatic lenses. See S. P. Thompson’s English translation, London, p. 114; 1912.
  8. M. L. Dunoyer: “Optique ondulatoire et optique géométrique,” Journ. de Phys., Ser. VI,  2, pp. 258–264; 1921.
  9. See Whewell’s edition of Barrow’s “Mathematical Works” (Cambridge, 1860), Lectiones opticæ,” Lect. XI, II, p. 96.
  10. The function denoted here by E is precisely the same as was employed in a previous paper by the author: Journ. Opt. Soc. Amer.,  4, pp. 294–299; 1920.
    [CrossRef]

1922 (1)

See J. O. S. A. & R. S. I.,  6, p. 293, 1922.
[CrossRef]

1921 (1)

M. L. Dunoyer: “Optique ondulatoire et optique géométrique,” Journ. de Phys., Ser. VI,  2, pp. 258–264; 1921.

1920 (1)

The function denoted here by E is precisely the same as was employed in a previous paper by the author: Journ. Opt. Soc. Amer.,  4, pp. 294–299; 1920.
[CrossRef]

1692 (1)

Molyneux’s “Dioptrica nova” (1692), pp. 42, 48, 63 and 68. Also article by Halley on “An Instance of the Excellence of the Modern Algebra, in the Resolution of the Problem of finding the Foci of Optick Glasses universally”: Phil. Transactions,  17, pp. 960–969; 1693.
[CrossRef]

Dunoyer, M. L.

M. L. Dunoyer: “Optique ondulatoire et optique géométrique,” Journ. de Phys., Ser. VI,  2, pp. 258–264; 1921.

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

See J. O. S. A. & R. S. I.,  6, p. 293, 1922.
[CrossRef]

Journ. de Phys. (1)

M. L. Dunoyer: “Optique ondulatoire et optique géométrique,” Journ. de Phys., Ser. VI,  2, pp. 258–264; 1921.

Journ. Opt. Soc. Amer. (1)

The function denoted here by E is precisely the same as was employed in a previous paper by the author: Journ. Opt. Soc. Amer.,  4, pp. 294–299; 1920.
[CrossRef]

Molyneux’s “Dioptrica nova” (1)

Molyneux’s “Dioptrica nova” (1692), pp. 42, 48, 63 and 68. Also article by Halley on “An Instance of the Excellence of the Modern Algebra, in the Resolution of the Problem of finding the Foci of Optick Glasses universally”: Phil. Transactions,  17, pp. 960–969; 1693.
[CrossRef]

Other (6)

Loc. cit., pp. 198, foll.

Œuvres complètes de Christiaan. Huygens publiées par la Société Hollandaise des Sciences. Tome treizième. Dioptrique. La Haye; 1916.

Loc. cit., pp. 40, foll.

See Whewell’s edition of Barrow’s “Mathematical Works” (Cambridge, 1860), Lectiones opticæ,” Lect. XI, II, p. 96.

Loc. cit., pp. 48, foll.

He makes the same statement again in his “Treatise on Light,” the last chapter of which is devoted to a discussion of the Cartesian ovals and the forms of aplanatic optical surfaces and aplanatic lenses. See S. P. Thompson’s English translation, London, p. 114; 1912.

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Figures (4)

Fig. 1
Fig. 1

Construction of Aplanatic Points J, J′ of a Spherical Refracting Surface: AC=r, CJ=nr, CJ′=r/n.

Fig. 2
Fig. 2

Aplanatic Glass Lens: AC=r, CJ=nr, CJ′=r/n (where n denotes index of glass).

Fig. 3
Fig. 3

Aplanatic Glass Lens: AC=r, CJ=r/n, CJ′=nr (where n denotes index of glass).

Fig. 4
Fig. 4

Huygens’ own diagram for showing construction of ray refracted at a spherical surface, by aid of aplanatic points D,S; reproduced from Fig. 27, Vol. XIII of Huygens’ Œuvres complètes, p. 63.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

i - r = C · i · sec r ,
C = n - 1 n ,
MF : MA = MC : M M ,
MF : MA = MA : M M .
Magnifying power = AB AK = ( c - u ) f u c + ( c - u ) f .
CJ = n · AC = n · r ,             n · C J = AC = r ;
CJ · C J = r 2 ;
n · P J - PJ = a constant ,
n · P J = PJ .
AJ A J = n = BJ J B ;
h k = r k · sin ( α k - θ k ) ,
n 1 · L 1 A 1 + n 2 · A 1 A 2 + n 3 · A 2 A 3 + + n m + 1 · A m L m + 1 ;
L 1 B 1 = h 1 sin θ 1 ,             B m L m + 1 = - h m sin θ m + 1 ,
B k B k + 1 = h k + 1 - h k sin θ k + 1 .
A 1 L 1 = v 1 ,             A m L m + 1 = v m ,
n 1 ( h 1 sin θ 1 + v 1 ) - n m + 1 ( h m sin θ m + 1 + v m ) + k = 1 k = m n k ( h k - h k - 1 sin θ k - d k - 1 ) .
- Σ n · p · E Π ,
α - θ = α - θ .
E = ( sin α - sin θ ) - ( sin α - sin θ ) = - 4 sin α - θ 2 · sin θ - θ 2 · sin α + θ 2 ; Π = 4 cos α 2 · cos α 2 · cos θ 2 · cos θ 2 .
n · p · E Π = n · h · sin θ · sin θ - θ 2 sin θ + θ 2 2 cos 2 θ 2 cos 2 θ 2 , ( r = ) .