focal distancen.

Brit.

/ˈfəʊkl ˌdɪst(ə)ns/, U.S.

/ˈfoʊk(ə)l ˌdɪstəns/

Origin: Formed within English, by compounding. Etymons: focal adj., distance n.

Etymology: < focal adj. + distance n.

1. Optics. The distance from a lens, lens system, or curved mirror to its focus along its focal axis; = focal length n. at focal adj. Compounds.In quot. 1850 in figurative context.

ΘΚΠ

the world > physical sensation > sight and vision > optical instruments > lens > [noun] > focal length or point

focus1664

focus1666

focal distance1684

focal point1692

burning-point1698

short focusa1830

visual focus1837

1684 W. Molyneux Let. 5 Jan. in J. Flamsteed Corr. (1997) II. 142 The sphere whose radius is the focal distance of the Objectglas.

1693 E. Halley in Philos. Trans. (Royal Soc.) 17 960 The focal distance sought.

1737 C. MacLaurin Let. 18 Feb. in Philos. Trans. 1737–8 (Royal Soc.) (1739) 40 180 Lord Aberdour made use of a reflecting Telescope of 15 Inches and a half focal Distance, that magnified 90 times.

1773 J. Watt Let. 27 Jan. in J. P. Muirhead Origin & Progress Mech. Inventions J. Watt (1854) II. 39 Could you make an achromatic lens of half an inch focal distance?

1850 R. W. Emerson Swedenborg in Representative Men iii. 104 A colossal soul, he lies vast abroad on his times..requires a long focal distance to be seen.

1879 G. C. Harlan Eyesight vi. 81 A double concave glass of twelve inches focal distance.

1915 Pop. Mech. Aug. 192/2 By..placing the plate a number of feet back of the lens and beyond the focal distance, an enlargement is obtained.

1981 Leonardo 14 296/1 Light leaving the set of prisms passes to a parabolic mirror that has a focal distance of at least 15 or 20 meters.

2011 PC World Mar. 73/2 With a minimum focal distance of 0.4 inch, it shines at extreme close-ups.

2. Geometry.

a. The distance between any given point of an ellipse or hyperbola and one of its foci. In early use also: the distance between the foci of an ellipse or a hyperbola and its centre (see centre n.¹ 10a).

ΘΚΠ

the world > relative properties > number > geometry > curve > [noun] > with regard to distance

focal length1682

focal distance1705

power of a point1872

curve or line of striction1875

the world > matter > physics > electromagnetic radiation > light > emission of light, radiation > [noun] > distance between centre and focus

focal distance1705

1705 H. Ditton Gen. Laws Nature & Motion i. 12 In order to the satisfying the Demands of the Problem, the Ellipses or Hyperbola's must be so proportion'd to each other, that their Transverse Axes may be in the Ratio assign'd, and their Focal Distances equal.

1787 C. Hutton Elements Conic Sections 54 The two semi-axes, and the focal distance from the center, are the sides of a right angled triangle.

1847 P. Barlow et al. Encycl. Pure Math. 758/2 The distance of any point from the focus is called the focal distance.

1888 Ann. Math. 4 167 The axes of an ellipse are given, and one focal distance of a point on the curve. Find the ordinate of the point drawn to the major axis.

1906 E. H. Askwith Analyt. Geom. Conic Sections ix. 157 The focal distances of the point P whose coordinates are ( x, y ) are a + ex, a −ex.

1968 Math. Mag. 41 236 Applying the focal-distance definition of a hyperbola to our first criterion, we have a second criterion for the nature of the conic on five given points.

2004 Jrnl. Atmospheric Sci. 61 2479/1 (caption) Here, c is the common focal distance of the ellipses and hyperbolas.

2012 T. M. Apostol & M. A. Mnatsakanian New Horizons Geom. viii. 254 The sum of focal distances..from a point on an ellipse to its foci is a constant.

b. The distance between any given point of a parabola and its focus. In early use also: the distance between the focus of a parabola and its vertex.

ΚΠ

1723 R. Steell Treat. Conic Sections i. 10 If, from the Focus, a Perpendicular be drawn to any Tangent; then the Square of that Line shall be equal to the Rectangle under the Focal Distance.

1758 Gen. Mag. Arts & Sci. June 348 Hence is deduced the best and easiest Method of describing the Curve of a Parabola, whose Focal Distance V F is given.

1813 J. M. Good et al. Pantologia Focal distance, the distance of the focus, which is sometimes understood as its distance from the vertex, as in the parabola.

1887 J. H. Smith Introd. Study Geom. Conic Sections ii. 12 The focal distance of a point within the parabola is less than the perpendicular distance of the point from the directrix.

1921 T. L. Heath Hist. Greek Math. II. xiv. 194 The tangent at any point makes equal angles with the axis and with the focal distance of the point.

2012 T. M. Apostol & M. A. Mnatsakanian New Horizons Geom. viii. 257 A parabola has only one focus F, and is the locus of a point P that moves in a plane with its focal distance PF always equal to its distance PD from a fixed line D.

This entry has been updated (OED Third Edition, September 2016; most recently modified version published online March 2022).

单词	focal distance
释义	focal distancen. Brit. /ˈfəʊkl ˌdɪst(ə)ns/, U.S. /ˈfoʊk(ə)l ˌdɪstəns/ Origin: Formed within English, by compounding. Etymons: focal adj., distance n. Etymology: < focal adj. + distance n. 1. Optics. The distance from a lens, lens system, or curved mirror to its focus along its focal axis; = focal length n. at focal adj. Compounds.In quot. 1850 in figurative context. ΘΚΠ the world > physical sensation > sight and vision > optical instruments > lens > [noun] > focal length or point focus1664 focus1666 focal distance1684 focal point1692 burning-point1698 short focusa1830 visual focus1837 1684 W. Molyneux Let. 5 Jan. in J. Flamsteed Corr. (1997) II. 142 The sphere whose radius is the focal distance of the Objectglas. 1693 E. Halley in Philos. Trans. (Royal Soc.) 17 960 The focal distance sought. 1737 C. MacLaurin Let. 18 Feb. in Philos. Trans. 1737–8 (Royal Soc.) (1739) 40 180 Lord Aberdour made use of a reflecting Telescope of 15 Inches and a half focal Distance, that magnified 90 times. 1773 J. Watt Let. 27 Jan. in J. P. Muirhead Origin & Progress Mech. Inventions J. Watt (1854) II. 39 Could you make an achromatic lens of half an inch focal distance? 1850 R. W. Emerson Swedenborg in Representative Men iii. 104 A colossal soul, he lies vast abroad on his times..requires a long focal distance to be seen. 1879 G. C. Harlan Eyesight vi. 81 A double concave glass of twelve inches focal distance. 1915 Pop. Mech. Aug. 192/2 By..placing the plate a number of feet back of the lens and beyond the focal distance, an enlargement is obtained. 1981 Leonardo 14 296/1 Light leaving the set of prisms passes to a parabolic mirror that has a focal distance of at least 15 or 20 meters. 2011 PC World Mar. 73/2 With a minimum focal distance of 0.4 inch, it shines at extreme close-ups. 2. Geometry. a. The distance between any given point of an ellipse or hyperbola and one of its foci. In early use also: the distance between the foci of an ellipse or a hyperbola and its centre (see centre n.¹ 10a). ΘΚΠ the world > relative properties > number > geometry > curve > [noun] > with regard to distance focal length1682 focal distance1705 power of a point1872 curve or line of striction1875 the world > matter > physics > electromagnetic radiation > light > emission of light, radiation > [noun] > distance between centre and focus focal distance1705 1705 H. Ditton Gen. Laws Nature & Motion i. 12 In order to the satisfying the Demands of the Problem, the Ellipses or Hyperbola's must be so proportion'd to each other, that their Transverse Axes may be in the Ratio assign'd, and their Focal Distances equal. 1787 C. Hutton Elements Conic Sections 54 The two semi-axes, and the focal distance from the center, are the sides of a right angled triangle. 1847 P. Barlow et al. Encycl. Pure Math. 758/2 The distance of any point from the focus is called the focal distance. 1888 Ann. Math. 4 167 The axes of an ellipse are given, and one focal distance of a point on the curve. Find the ordinate of the point drawn to the major axis. 1906 E. H. Askwith Analyt. Geom. Conic Sections ix. 157 The focal distances of the point P whose coordinates are ( x, y ) are a + ex, a −ex. 1968 Math. Mag. 41 236 Applying the focal-distance definition of a hyperbola to our first criterion, we have a second criterion for the nature of the conic on five given points. 2004 Jrnl. Atmospheric Sci. 61 2479/1 (caption) Here, c is the common focal distance of the ellipses and hyperbolas. 2012 T. M. Apostol & M. A. Mnatsakanian New Horizons Geom. viii. 254 The sum of focal distances..from a point on an ellipse to its foci is a constant. b. The distance between any given point of a parabola and its focus. In early use also: the distance between the focus of a parabola and its vertex. ΚΠ 1723 R. Steell Treat. Conic Sections i. 10 If, from the Focus, a Perpendicular be drawn to any Tangent; then the Square of that Line shall be equal to the Rectangle under the Focal Distance. 1758 Gen. Mag. Arts & Sci. June 348 Hence is deduced the best and easiest Method of describing the Curve of a Parabola, whose Focal Distance V F is given. 1813 J. M. Good et al. Pantologia Focal distance, the distance of the focus, which is sometimes understood as its distance from the vertex, as in the parabola. 1887 J. H. Smith Introd. Study Geom. Conic Sections ii. 12 The focal distance of a point within the parabola is less than the perpendicular distance of the point from the directrix. 1921 T. L. Heath Hist. Greek Math. II. xiv. 194 The tangent at any point makes equal angles with the axis and with the focal distance of the point. 2012 T. M. Apostol & M. A. Mnatsakanian New Horizons Geom. viii. 257 A parabola has only one focus F, and is the locus of a point P that moves in a plane with its focal distance PF always equal to its distance PD from a fixed line D. This entry has been updated (OED Third Edition, September 2016; most recently modified version published online March 2022). < n.1684
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