focaladj.
/ˈfəʊkl/, U.S. /ˈfoʊkəl/ΚΠ
1639 T. Phillips Bk. Lament. 20 The Schoolemen hold, the fire of Hell to be..of the same kind with our fire both Elementarie and culinarie or focal.
1699 G. Harvey Vanities Philos. & Physick vii. 51 The Air in ventilating the focal Fire, or any burning flame, doth assist its most subtil particles in separating and expelling fuliginous and other corpuscles.
a1763 J. Byrom Misc. Poems (1773) I. 110 When his Letter came, Some Friends were chair'd around the focal Flame.
1848 H. Barnard School Archit. 162 The common domestic focal fire may not..be relied upon as a means of ventilating an apartment in connection with open windows.
2. Geometry. Designating a geometric figure intersecting or otherwise described relative to a focus or foci (esp. of a conic section); of, relating to, or having a focus or foci. See also Compounds.
ΘΚΠ
the world > relative properties > number > geometry > shape or figure > [adjective] > having specific property
hypotenusal?a1560
oblique?a1560
local1673
focal1676
octantal1777
symmetrical1794
radical1848
self-conjugate1855
quadric1856
stellated1859
periphractic1881
homoeoidal1883
tridiametral1891
one-sided1893
semi-infinite1903
simplicial1913
mirror-symmetric1952
1676 E. Halley Let. 8 July in H. Oldenburg Corr. (1986) XII. 370 The rule for finding the length of any focall ray of an Ellipsis the Transvers diam, distance of the foci and the angle made with the transverse diameter being given.
1804 J. Robison Elements Mech. Philos. 359 An equation expressing the focal chord of curvature is as distinctive as the usual equation, and leads us with ease to the chief properties of the figure.
1842 London, Edinb., & Dublin Philos. Mag. 21 437 The point of concourse of the tangents at the extremities of two focal radii vectores, which contain between them a constant angle, will generate a conic section.
1871 Trans. Royal Irish Acad.: Sci. 24 485 The centres of any two of the three circles of inversion of a Cartesian oval are the limiting points of its third circle of inversion and the corresponding focal circle.
1961 New Scientist 9 Nov. 380/2 The tangents at the extremities of a focal chord intersect at right angles on the directrix.
2012 P. Lockhart Measurement 181 It is the sum of these distances that provides the focal constant for an ellipse.
3. Optics. Of or relating to a focus of a lens, mirror, or other optical system (see focus n. 5a); collected or situated at a focus of reflected or refracted radiation (see focus n. 5b). Also: of or relating to focusing an optical system. See also Compounds, focal point n. 1b.Recorded earliest in focal length n. at Compounds.In quot. 1860 in figurative context.
ΘΚΠ
the world > matter > physics > electromagnetic radiation > light > emission of light, radiation > [adjective]
focal1682
aberrational1837
focalizing1838
the world > matter > physics > electromagnetic radiation > heat > [adjective] > radiation > focus
focal1794
the world > physical sensation > sight and vision > seeing or looking > [adjective] > looking at or beholding > focusing
focalizing1838
focal1855
1682 J. Flamsteed Let. 7 July in Corr. (1997) II. 17 The distinctnesse is as the focall length of the one object glasse is to the like length of the other.
1692 W. Molyneux Dioptrica Nova i. 36 If the Rays fall very obliquely,..they are scattered and the Focal Depth is very great.
1717 J. T. Desaguliers in Philos. Trans. 1714–16 (Royal Soc.) 29 439 The focal place, where the red part of the Image is distinct.
1794 G. Adams Lect. Nat. & Exper. Philos. II. xv. 197 You may, by means of the focal rays from this glass, char or burn a piece of wood.
1855 H. Spencer Princ. Psychol. iii. xi. 452 Perfect vision implies a focal adjustment of the eyes.
1860 C. Patmore Faithful for Ever 214 Love requires the focal space Of recollection or of hope, Ere it can measure its own scope.
1920 Amer. Naturalist 54 514 It is often impossible to secure adequate photomicrographs of hair shafts, since it is necessary to employ high-powered objectives with a consequent very limited focal depth.
1979 Philos. Trans. (Royal Soc.) A. 292 149 Microfocus X-ray tubes..have been developed with focal spots between 10 and 100 μm.
2001 Outdoor Photographer Aug. 32 (advt.) The compositional flexibility of a 7× optical zoom lens, with the 35mm equivalent of a 28-200mm focal range.
4. figurative and in extended use. Characterized by or exhibiting the convergence or concentration of a number of different elements; (now usually) of central importance or interest. Cf. focus n. 6a.Recorded earliest in focal point n. 2.
ΘΚΠ
the world > space > relative position > inclination > state or quality of being convergent > [adjective] > composed of or formed by things converging
focal1755
convergent1831
1755 E. Young Centaur v. 283 Human thought..whose scattered rays must be collected, as it were, to a focal point, in order duly to warm our devotion.
1776 London Rev. Eng. & Foreign Lit. Oct. 277 This substance..generates our senses, our passions, our habits, our volitions..; in short, that whole focal concentration of life.
1842 Westm. Rev. Oct. 189/1 That focal centre where all the facts and series of facts that constitute the history of nations..converge into unity.
1894 C. L. Morgan Introd. Compar. Psychol. i. 17 We..pay attention solely to focal consciousness, omitting all reference to the great body of marginal subconsciousness.
1967 Daily Tel. 21 Feb. 16/3 These people, ‘writers, musicians, psychedelic popsters and hippies..’ see London as a ‘focal city for permissive experiments’ in art and life.
2013 Guardian 5 July (G2 section) 23/3 The focal line of this lubricious party jam is ‘I know you want it’, repeated over and over.
5. At or relating to the centre or place of origin of a natural phenomenon or process, such as volcanic activity or an earthquake, the dispersal or radiation of a species, etc.
ΘΚΠ
the world > space > relative position > central condition or position > [adjective] > situated in the centre or middle
mideOE
middleeOE
mean1340
midwarda1400
moyen1481
centrica1593
midway1608
centricala1631
umbilical1742
middling1747
median1771
focal1825
1825 G. P. Scrope Considerations on Volcanos ii. 47 This gradual augmentation of temperature in the focal mass must proportionately increase the expansive force of the elastic fluids it contains.
1862 G. P. Scrope Volcanos (ed. 2) 264 The residuum of..lava..in what may be called its focal reservoir.
1869 London Q. Rev. Jan. 58/1 The focal cavity, when at its full dimensions, was a curved fissure, whose height was three geographical miles.
1926 Pop. Mech. Apr. 592/2 Storm areas have certain definite focal centers and follow certain paths as the seasons change.
1970 Jrnl. Brit. Astron. Assoc. 80 197 The focal development of minor volcanic cones is a well-known volcanic pattern.
2014 M. Lamontagne & G. Ranalli Intraplate Earthquakes iv. 87 Numerous sub-zones, each one with its special focal depth distribution, level of activity, and focal mechanism complexity.
6. Medicine. With reference to disease, inflammation, abnormal physiological activity, etc.: of the nature of or arising from a focus (focus n. 4); localized; restricted in extent.
ΚΠ
1854 Amer. Jrnl. Med. Sci. 28 418 The ‘focal points’ of external neuralgia are generally in the following situations.
1889 Lancet 16 Feb. 322/1 The fits for the last year and a half of his life..gave no clue to any focal brain lesion.
1902 Brit. Med. Jrnl. 29 Nov. 1709/1 The source of hæmatemesis might be focal—as from a single large vessel—or diffuse.
1946 Lancet 9 Nov. 676/2 They found discrete acellular areas of focal necrosis, as well as diffuse necrosis with astroglial reaction, in the cerebrum.
1993 S. J. Ettinger Pocket Compan. Textbk. Vet. Internal Med. xlix. 169 Radiographs are useful in demonstrating fungal osteomyelitis and discospondylitis in focal disease and in nearly all cases of disseminated disease.
2011 Vanity Fair Jan. 62/2 They were given a variety of new drugs to treat everything from high blood pressure to chronic focal encephalitis, a brain inflammation that causes epileptic seizures and other neurological problems.
Compounds
focal aperture n. Optics and Photography (a) the aperture at the focal plane of a telescope or other optical instrument (now rare); (b) a measure of the light-collecting power of a lens, telescope, etc.; = relative aperture n. at relative n., adj., and adv. Compounds.
ΚΠ
1841 Civil Engineer & Architect's Jrnl. 4 424/1 For instance, the diaphragm or focal aperture of a 20 inch telescope is ·39 inches.
1910 Nature 20 Jan. 339/1 In the common focal plane of the telescope objective and eye-piece,..a small totally reflecting prism is arranged, half covering the focal aperture.
1956 T. L. Gunn Photogr. in Garden iv. 43 To..secure reasonable definition on a windy day, it may be necessary to effect a compromise between exposure and the most effective focal aperture.
1986 Proc. SPIE (Internat. Soc. Optical Engin.) 645 85 The focal aperture of these lenses is around F/2.5 although faster lenses ~F/1 are routinely manufactured utilising the same techniques.
2013 Geospatial Today (Nexis) 27 Sept. Also, it is possible to track tiny bodies using telescopes with large focal aperture.
focal axis n. (a) Geometry the line passing through the focus or foci of a conic section, perpendicular to the directrix; (b) Optics the line which passes through the focal point (or points) of a curved mirror or lens and its centre; the line which passes through the centre of each lens in a compound lens, telescope, microscope, or other optical instrument; cf. axis n.1 9a.
ΘΚΠ
the world > relative properties > number > geometry > geometric space > [noun] > division or marking of > axis > passing through foci
principal axis1704
transverse axis1704
transverse1743
longitudinal axis1744
focal axis1794
major axis1840
1794 G. Walker Treat. Conic Sections i. 58 Let A then be a point in the plane of a conic section, whose focus is F, directrix XX, and semi-parameter of the focal axis Z.
1828 C. Rumker in Mem. Astron. Soc. London (1829) 3 ii. 278 A telescope placed at the distance of six feet, so that its focal axis, produced, touched the screen and passed through the wire and cross when at rest.
1838 C. Tomlinson Stud. Man. Nat. Philos. ix. 416 The refracted rays..congregate, and produce upon the eye of the observer, placed in the focal axis, a greatly increased impression.
1885 C. Leudesdorf tr. L. Cremona Elements Projective Geom. 255 The point in which a directrix cuts the focal axis.
1905 Canad. Patent Office Rec. 2451/1 An arc lamp having its carbons disposed at an angle with the focal axis of the reflector.
1948 Amer. Math. Monthly 55 156 Our purpose is to examine the possibility of exhibiting the ellipse as the locus of a point on a rotating circle with a center moving on the focal axis.
2003 Physiol. & Biochem. Zool. 76 362/2 The middle web of each foot..was the web most consistently held perpendicular to the focal axis of the camera by the birds.
2011 Math. Mag. 84 91 The second focal circle now becomes a line perpendicular to the focal axis, which we call a floating focal line.
focal capacity n. Optics and Photography the maximum (or minimum) focal distance of a lens or lens system, or of an optical instrument or camera.
ΚΠ
1882 Amer. Naturalist 16 346 This is a glass slide with an attached cell..raised by a glass disk, so that the bottom of the cell will be within reach of the focal capacity of the objective used.
1906 Camera Aug. 293/2 The focal capacity of the camera, including cone extension, is 7½ feet.
2007 M. Antliff Avant-garde Fascism iv. 197 Eisenstein's portrait shocks the viewer..by bringing the camera closer than the focal capacity of her lens, which necessarily results in extreme blur.
focal conic n. Geometry (now rare) any of the several conics formed in each of the principal planes of a quadric surface by its foci.
ΚΠ
1842 London, Edinb., & Dublin Philos. Mag. 21 64 Let the points on the focal conic, at which the tangent is parallel to the trace of the tangent plane, be considered analogous to foci.
1874 Messenger Math. 3 132 Suppose we describe all the quadrics which have given focal conics. Begin with the ellipsoid of infinite size, and let its axes diminish.
1960 W. H. McCrea Anal. Geom. Three Dimensions (rev. ed.) 134 Every point of the conic..lying in the plane ζ = 0 is a focus; this is called a focal conic.
focal curve n. Geometry rare a curve formed by the centres of curvature of another curve; = evolute n. 1a.
ΚΠ
1828 Trans. Royal Irish Acad. 15 Science 77 Plane curves having a given caustic; focal curves.
1929 Philos. Trans. (Royal Soc.) A. 228 338 The locus of the foci we call the ‘focal curve’.
2002 N. M. Patrikalakis & T. Maekawa Shape Interrogation viii. 203 For a parametric space curve r ( t ), a focal curve or an evolute..is defined as f ( t ) = r( t ) + n( t )/κ.
focal length n. the distance from a lens, lens system, or curved mirror to its focus along its focal axis; = focal distance n. 1.
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
1682Focall length [see sense 3].
1682 J. Flamsteed Let. 7 July in Corr. (1997) II. 17 The distinctnesse is as the focall length of the one object glasse is to the like length of the other.
1732 S. Fuller Pract. Astron. 154 The Radius of the Sphere, on which the Concave Metalline Speculum must be ground.., will be about Ten Feet, and consequently its Focal Length will be about 62 Inches.
1754 Philos. Trans. 1753 (Royal Soc.) 48 170 An object-lens whose focal length is a little less.
1831 D. Brewster Treat. Optics xlii. 357 The great speculum has a focal length of 25 feet, and a diameter of 15 inches.
1940 N.Y. Times 1 Sept. x. 5/1 Most amateurs dream of owning a huge battery of lenses—as many as ten or twenty—of differing focal lengths.
1992 Irish Times 9 Jan. 9/4 The project involved testing the mirror's focal length so that fine adjustments to its surface could be made.
2005 TNT Mag. 7 Mar. 83/2 The angle of view depends on the focal length of the lens and the film format/digital setting.
focal line n. Geometry (a) a line which intersects with or terminates in the focus of a geometric figure; †(b) the focal conic of the cone which consists of two intersecting lines, regarded as a degenerate hyperbola (obsolete rare).
ΚΠ
1794 G. Walker Treat. Conic Sections i. 101 The rectangular under the segments of each between the focus and section or sections, shall be to each other as the segments of the focal lines, intercepted between the section or sections.
1862 G. Salmon Treat. Analytic Geom. Three Dimensions vii. 104 The focal lines of the cone..are plainly the asymptotes to the focal hyperbola of the surface.
1871 Dublin Exam. Papers for 1870 23 The angle between one tangent and one focal line is equal to the angle between the other tangent and the other focal line.
2009 D. Kalman Uncommon Math. Excursions vi. 121 With calculus and analytic geometry, we can find the equations of the ellipse, tangent, and focal lines.
focal property n. Geometry any of various properties of a geometric figure that involve its focus or foci; esp. (a) the property that the lines though any point of an ellipse or hyperbola and its foci make equal angles with the tangent at that point; (b) the property that the line though any point on a parabola and its focus and the line that is parallel to the axis and runs through the same point make equal angles with the tangent at that point.
ΚΠ
1813 J. M. Good et al. Pantologia at Conic Sections Therefore FM = x + 1/2 c = AP + AF; which is the chief focal property of the parabola.
1840 J. Booth in London, Edinb., & Dublin Philos. Mag. 17 432 (title) On the focal properties of surfaces of the second order.
1867 W. Thomson & P. G. Tait Treat. Nat. Philos. I. i. 9 In drawing an ellipse, the focal property of the curve shows us that by fixing the ends of such a cord to the foci and keeping it stretched by a pencil, the latter will trace the curve.
1933 Math. Gaz. 17 278 The opening chapter deals with radial properties of the circle and focal properties of conic sections.
2012 P. Lockhart Measurement 179 There is a very pretty connection between these tangent lines and the focal property of the hyperbola.
focal ratio n. †(a) Mathematics the ratio of the distances from a given point on a conic section to its directrix and to one of its foci (obsolete rare); (b) the ratio of the focal length of a lens, telescope, etc., to the effective diameter of the aperture, used typically to express its light-gathering power; = f-number n. at F n. Additions.
ΚΠ
1835 S. W. Waud Treat. Algebraical Geom. Contents p. xiv From the position of the directrix and focus, and focal ratio, to find the equation to the curves of the second order.
1883 Eng. Mechanic & World of Sci. 38 259/2 A correction is applied to the focal ratio for removing dispersion, which may possibly improve the achromatism.
1945 Pop. Mech. Jan. 148/2 Such a lens was finally designed by Dr. W. B. Rayton..that gave excellent definition with a focal ratio of f:0.6.
2005 R. B. Thompson & B. F. Thompson Astron. Hacks i. 76 Large refractors usually have short focal ratios to allow reasonable tube lengths of a meter or so.
focal surface n. (a) Geometry a surface formed by the centres of curvature of a surface; = evolute n. 1a; (b) Optics an imaginary curved (usually spherical) surface on which initially parallel rays come to a focus after passing through a given lens or other optical system, and on which (in the case of visible light) the images of distant objects would be formed.In the latter sense, a focal surface with no curvature is a focal plane.
ΘΚΠ
the world > relative properties > number > geometry > curve > [noun] > locus
locus1675
evolute1704
place1704
trajectory1795
syntractory1820
focal surface1828
synharmonic1850
syntractrix1852
pedal1862
umbilical focal conic1862
umbilical focal conic1862
stigmatic1863
synchronism1867
synchronous curve1867
Steinerian1873
tac-locus1873
strophoid1880
orthoptic locus1882
strophoidal1908
hypercycle1909
1828 Trans. Royal Irish Acad. 15 Science 128 Contact of the third order, between the given mirror and its osculating focal surface.
1893 Proc. Royal Soc. 1892–3 52 408 Any want of definition at the margin will be chiefly due to curvature of the focal surface.
1912 Publ. Astron. Observatory Univ. Mich. 1 39/1 Plaskett has found this lens to be remarkably free from spherical aberration over a wide range of its unusually flat focal surface.
1922 F. Woods Higher Geom. iv. xvii. 338 Any line of the congruence is tangent to the focal surface.
2001 J. Gallier Geom. Methods & Applic. 651 The focal surfaces Y and Z are generated by the lines of strictions of the developable surfaces generated by the normals to the lines of curvatures.
2003 N. James & G. North Observing Comets vii. 151 The film must be held against a specially shaped focal plate so that it forms the correct shape to match the focal surface.
ΘΚΠ
the world > relative properties > number > geometry > line > [noun] > tangent
touchline1551
adscript1636
tangent1655
focal tangent1706
semi-tangent1823
tractor1867
bitangent1873
slope1889
1706 W. Jones Synopsis Palmariorum Matheseos 249 Sup. any Ordinate mr, of an Ellipse, to meet the Focal Tangent.
1773 Philos. Trans. (Royal Soc.) 63 355 Let DΣ be any Ordinate to the axe Aa, cutting the curve in Σ, and the focal tangent ΦG in σ.
1871 Messenger Math. 5 136 Let δ be the distance from the focus to the point of contact of the focal tangent.
ΘΚΠ
the world > relative properties > number > geometry > curve > [noun] > locus
locus1675
evolute1704
place1704
trajectory1795
syntractory1820
focal surface1828
synharmonic1850
syntractrix1852
pedal1862
umbilical focal conic1862
umbilical focal conic1862
stigmatic1863
synchronism1867
synchronous curve1867
Steinerian1873
tac-locus1873
strophoid1880
orthoptic locus1882
strophoidal1908
hypercycle1909
1862 Q. Jrnl. Math. 5 371 Since the umbilici U, V are the points in which the umbilical focal conic cuts the ellipsoid, and the umbilical focal conic is the limit of a confocal hyperboloid, it follows that the umbilici may be regarded as a line of curvature.
1886 P. Frost Solid Geom. (ed. 3) 147 The fixed point is called an umbilical focus..and the locus of the focus the umbilical focal conic.
Derivatives
ˈfocally adv. at a focus; in a focused manner.
ΘΚΠ
the mind > attention and judgement > attention > earnest attention, concentration > [adverb] > at a focus
focally1770
1770 P. Skelton Wks. IV. xxix. 570 Every one knows how the sun-beams operate on the vegetable and animal creation... In like manner, true religion..may, by meditation and devotion, be so focally collected.
1854 T. De Quincey On War in Select. Grave & Gay IV. 282 The force of European opinion, focally converged upon the subject.
1953 R. W. Fairbrother Text-bk. Bacteriol. (ed. 7) xi. 158 Delayed reactions may occur locally at the site of inoculation, focally at the focus of infection and also generally.
2008 A. R. Prasad et al. in J. Jankowski et al. Gastrointestinal Oncol. x. 283/2 The lesion is typically very large, pedunculated and covered by an intact smooth mucosal surface that can be focally ulcerated.
This entry has been updated (OED Third Edition, September 2016; most recently modified version published online March 2022).
<
adj.1639