Pl. foci; also focuses, in England usually written irregularly focusses. [a. L. focus hearth, fireplace, in various modern uses.
The Lat. word was first used in sense 1 by Kepler (Astron. pars optica, iv. 4, written in 1604); his reason for the choice of the name is not stated, but it is conjectured that the optical sense 2, ‘burning point of a lens or mirror’ (which is easily derived from the lit. sense) must have been already in existence; this would account for Kepler’s use, as the ‘burning point’ or ‘focus’ of a parabolic mirror is situate at the geometrical ‘focus’ of its curvature. Sense 4 is from medical Latin. In all senses cf. Fr. foyer:—L. *focārium f. focus.]
1. Geom. a. In plane geometry: One of the points from which the distances to any point of a given curve are connected by a linear relation.
Also defined as a point from which a pair of isotropic tangents can be drawn to a curve; or as the intersection of tangents from the points in which the line at infinity meets a co-planar circle. (For definitions specially relating to the focus of a conic, see quots. 1881 and 1893.)
1656. Hobbes, Six Lessons, Wks. 1845, VII. 317. The focus of an hyperbole, is in the axis, distant from the vertex, as much as the hypotenusal of a rectangled triangle, whose one side is half the transverse axis.
1703. Moxon, Mech. Exerc., 272. Which two points are called the Focusses, or burning points.
1734. trans. Maupertuis’ Diss., 19, in Keill’s Exam. (1734), 19. The Orbits of the Planets are not Circles, but Ellipses, in whose Focus the Sun is.
1807. Hutton, Course Math., II. 96. The ellipse and hyperbola have each two foci; but the parabola only one.
1851. Nichol, Archit. Heav., 199. The one star seems to move around the other, not in a circle, but an ellipse, the second star being in the focus, and not the centre of the ellipse.
1881. C. Taylor, Geom. Conics, 1. A Conic Section, or, briefly, a Conic, is a curve traced by a point which moves in a plane containing a fixed point and a fixed straight line in such a way that its distance from the fixed point is in a constant ratio to its perpendicular distance from the fixed straight line…. The fixed point is called a Focus.
1893. J. W. Russell, Pure Geom., vii. 67. A focus of a conic is a point at which every two conjugate lines are perpendicular.
b. In solid geometry (see quot.).
1874. G. Salmon, Analytic Geom. (ed. 3), 109. We may thus define a focus as a point through which can be drawn two lines σ, each touching the surface and the imaginary circle at infinity, and such that the tangent plane to the surface through either also touches the circle at infinity.
2. Optics, Heat, etc. The point at which rays meet after being reflected or refracted; also, the point from which the rays appear to proceed (= virtual focus: see 2 b).
1685. Boyle, Effects Motion, ii. 13. [Sun-beams] being refracted or reflected, by a burning glass to a focus, they by their concourse, compose a small portion of fluid matter, so violently agitated, as to kindle green wood in less than a minute, and to melt not only tin and lead, thinly beaten, but leaf-silver and gold.
1704. Newton, Opticks, I. vi. 7. The Point from which Rays diverge or to which they converge may be called their Focus.
1831. Brewster, Optics, i. 11. The points that were formerly the radiant points being now the foci.
1853. Herschel, Pop. Lect. Sc., ii. § 24 (1873), 65. It turns out to be more than 90,000 times greater than the intensity of sunshine here on our globe at noon and under the equator—a far greater heat than can be produced in the focus of any burning-glass.
1865. Livingstone, Zambesi, ii. 59. This deep trough-like shape caused the sun’s rays to converge as into a focus, making the surface so hot that the soles of the feet of the Makololo became blistered.
b. With various defining words.
Conjugate foci: see CONJUGATE a. 6 b; principal focus, the point at which parallel rays meet after passing through a convergent lens; solar focus = prec.; virtual focus, a point at which diverging rays would meet if their directions were reversed; actinic or chemical focus (of a lens), the point to which the actinic rays converge.
1706. Phillips (ed. Kersey), Virtual Focus, or Point of Divergence (in Dioptricks).
1812–6. J. Smith, The Panorama of Science and Art, I. 426. When parallel rays fall upon a double convex glass, KG, they will be refracted still more abruptly, and meet sooner in a point or principal focus at F.
1874. trans. Lommel’s Light, 90. The lenses of the second group have virtual foci; they make parallel rays divergent, divergent still more divergent, convergent less convergent, or even divergent.
1890. Woodbury, Encycl. Photogr., 293. Unless the lens be rendered achromatic the actinic or chemical focus does not coincide with the visual focus.
c. transf. and fig.
1762. Goldsm., Cit. W., lxxi. A box where they might see and be seen; one, as they expressed it, in the very focus of public view.
1781. Cowper, Conversation, 239.
| There centering in a focus, round and neat, | |
| Let all your rays of information meet. |
1824. Carlyle, in Froude, Life (1882), I. 260. I am meditating with as rigid an intensity as ever on the great focus of all purposes—the arranging of my future life.
1874. Micklethwaite, Modern Parish Churches, 106. If it [a picture] be placed over the altar, it is in the very focus of the building, and is certain to usurp the place of the altar, and become the most important object in the church.
† d. Theatr. The best-illuminated part of the stage. Obs.
1881. H. Irving, Does Punch feel? in Era Almanack, 97. D—— the fellow, he tried to keep me out of the focus!
1885. Eng. Illustr. Mag., 647/1. Every body tried to get into what was called the focus—the ‘blaze of publicity’ furnished by the ‘float’ or footlights.
e. That point or position at which an object must be situated, in order that the image produced by the lens may be clear and well-defined. Hence in, or out of focus, lit. and fig. Depth of focus (of a lens): the power of giving a ‘sharp’ image of objects not in the same plane.
1713. Derham, Phys. Theol., IV. ii. 89, note. If the Paper that receives the Images be too nigh, or too far of the Lens, the Image will be confused and dim; but in the Focus of the Glass, distinct, clear, and a pleasant Sight.
1727. Swift, Petit. Colliers &c., Wks. 1755, III. I. 129. To know the due distances of the said focus’s, or fires, and to adjust the position of their glasses to the several altitudes of the sun.
1799. Med. Jrnl., II. 228. Let the pressure be made on the external angle of both eyes, at the same time, whilst the sight is directed straight forwards, and downwards to any object, at the nearest focus of distinct vision.
1840. Dickens, Barn. Rudge, i. John gradually concentrated the whole power of his eyes into one focus, and brought it to bear upon the man in the flapped hat.
1858. A B C of Photogr. (ed. 10), 48. The focus of a portrait lens is very limited in depth; that is, it will not produce sharp and well-defined images of objects which are at different distances from the camera.
1890. Woodbury, Encycl. Photogr., 295. After a certain distance all objects will be in focus.
1894. H. Drummond, Ascent of Man, vi. Evolution was given to the modern world out of focus, was first seen by it out of focus, and has remained out of focus to the present hour.
f. To bring, etc., vin, into, to a focus; lit. and fig.
1788. Franklin, Autobiog., Wks. 1840, I. 122. The bringing all these scattered counsels into a focus enabled them to make greater impression.
1860. Tyndall, Glac., II. xxiv. 354. I placed a large converging lens in the sunbeams passing through a room, and observed the place where the rays were brought to a focus behind the lens.
1875. Jevons, Money (1878), 252. By the intervention of the banker, however, the transactions of many different individuals, or even of many branches of trade, are brought to a focus, and a large proportion of payments can be balanced off against each other.
g. The focal length (of a lens); also, the adjustment (of the eye, or an eyeglass) necessary to produce a clear image.
1693. E. Halley, in Phil. Trans., No. 205. 960. This dioptric problem, is that of finding the focus of any sort of lens.
1757. Ellis, ibid., L. 287. A lens of about one inch and half focus.
1837. Brewster, Magnet., 334. The focus of the lens being suited to the distance of the needle.
1861. Palgrave, Gold. Treas., Preface. The English mind has passed through phases of thought and cultivation so various and so opposed during these three centuries of Poetry, that a rapid passage between Old and New, like rapid alteration of the eye’s focus in looking at the landscape, will always be wearisome and hurtful to the sense of Beauty.
1871. Tyndall, Fragm. Sc. (1879), I. ii. 50. The focus was attained, first by the pupil and afterwards by the retina.
3. Similarly in Acoustics. The point or space towards which the sound waves converge.
1644. Evelyn, Diary, 8 Feb. Standing at one of the focus’s, which is under a tree, or little cabinet of hedges, the voice seems to descend from the clouds.
1843. J. Martineau, Chr. Life, xliii. (1876), 499. Could we only find the focus of those stray tones, we should understand more than any knowledge can tell.
1857. Thoreau, Maine W. (1894), 362. The loon being in a regularly curving bay under the mountain, we were exactly in the focus of many echoes, the sound being reflecgted like light from a concave mirror.
4. Of a disease: The principal seat (in the body); also, a point where its activity is manifest.
1684. trans. Bonet’s Merc. Compit., VI. 183. That the focus of burning fevers is in the Head Hippocrates seems to assert.
1796. H. Hunter, trans. St. Pierre’s Studies of Nature (1799), III. 231. She informed me that the focus of my disorder was in the nerves.
1854. Jones & Siev., Pathol. Anat. (1874), 304. Sclerosis of particular regions or isolated foci occurs in the cord as in the brain.
5. The center of activity, or area of greatest energy, of a storm, volcanic eruption, etc.
1796. H. Hunter, trans. St. Pierre’s Studies of Nature (1799), I. p. lx. The focus of the tides is removing farther and farther from our coasts.
1804. C. B. Brown, trans. Volney’s View Soil U. S., 98. It forms one of the great layers of the country, where earthquakes have their principal focus.
1832. Lyell, Princ. Geol., II. 127. The original isle was the primitive focus, or centre, of a certain type of vegetation, whereas, in the surrounding isles, there would be a smaller number of species, yet all belonging to the same group.
1862. G. P. Scrope, Volcanos, 266. Any particular focus or reservoir of lava from which an eruption has proceeded may be wholly consolidated.
1869. Phillips, Vesuv., ii. 13. Vesuvius was seen to be the focus of the eruption, which, it appears by modern research, had caused the ruin of the whole south-western part of the mountain.
1875. Bedford, Sailor’s Pocket-bk., iv. (ed. 2), 78. The average rate of the progressive movement of the centre or focus of the West Indian hurricanes is about 300 miles a day.
b. fig. A center or ‘hotbed’ (of intrigue, sedition, etc.); a center of activity or energy.
1808. Wellington, in Gurw., Desp., II. 440. Poonah is the focus of his intrigues, and he is worked upon by the reports which come from thence.
1830. R. Knox, Béclard’s Anat., p. viii. The Central Schools, which had been established in the departments as so many foci of knowledge, destined to enlighten a regenerated nation, were then in full activity.
1837. W. Irving, Capt. Bonneville, I. Introd., 10. Full of that buoyant hope, however, which belongs to the sanguine temperament, he repaired to New York, the great focus of American enterprise, where there are always funds ready for any scheme, however chimerical or romantic.
1870. Huxley, Lay Serm. i. (ed. 5), 5. The principal focus of scientific activity in our islands, and the chief champion of the cause it was formed to support.
6. nonce-uses. a. In Lat. sense: A fireplace or furnace; in quot. fig. b. A center of radiant heat.
1779. J. Moore, View Soc. Fr., I. xx. 176. I consider these men as the enemies of their country, and that place as a focus for consuming freedom.
1794. J. Hutton, Philos. Light, etc., 174. Those surrounding particles receiving that addition of heat from the focus, are made to burn; and in burning, these coals return that heating species of light to the focus, for the increase of its burning.
7. attrib., as focus point, error.
1891. Pall Mall G., 31 Aug., 2/1. That all railway servants shall have … not more than an agreed amount of focus error.
