Focus
Collier's New Encyclopedia (1921)
in ordinary language, any place from which an influence emanates, or where that influence exists in very concentrated form. In optics, a point at which the rays of light refracted from a convex lens, or reflected from a concave mirror, are most concentrated; a point in which such rays meet, or tend to meet; if produced either backward or forward. In conic sections: (1) Singular (of a parabola): A point so situated that if from it there be drawn a line to any point in the curve, and another from the latter perpendicular to a straight line given in position, these two straight lines will always be equal to one another. (2) Plural: (a) Of an ellipse: Two points so situated that if two straight lines be drawn from them to any point in the curve, the sum of these straight lines will always be the same. (b) Of a hyperbola: Two points so situated that if two straight lines be drawn from them to any point in the curve, the excess of the straight line drawn to one of the points above the other will always be the same. In astronomy, the term foci is often used in connection with the orbit of the earth, which is an ellipse, with the sun in one of the foci. In acoustics, the point of convergence of sound rays, these following the same laws as those of light and heat. Acoustic focus: The focus of sound rays. Calorific focus: The focus of heat rays. Conjugate foci: In optics, two foci so situated that, if rays of light diverging from one strike a concave mirror, they will be reflected and meet in the other. Luminous focus: In optics, the focus of light rays. Principal focus: In optics, the focus of parallel rays striking a concave mirror. Vertical focus: In optics, a radiant point behind a mirror, from which rays may be held to diverge more and more, and in which, looking at them now as coming from the opposite direction, and consequently as convergent, they would tend to meet. Magnetic foci: The two points on the earth's surface where the magnetic intensity is greatest; they nearly coincide in position with the magnetic poles.
What Has Changed in the Last Century
The optical and geometrical definitions Collier's gave in 1921 are still exactly what a student learns today: the focus of a lens or mirror, the single focus of a parabola, the two foci of an ellipse and hyperbola, and the sun sitting at one focus of the earth's orbit. Some of the vocabulary has quietly fallen out of use — "calorific focus" and "luminous focus" are no longer taught as separate terms, and "focal point" now does most of the everyday work. The one item that has genuinely dated is the last line on "magnetic foci": the magnetic poles wander, and the north magnetic pole has drifted out of the Canadian Arctic and across toward Siberia since 1921, moving fast enough that the world magnetic model has to be revised every few years. The word has also spread into fields Collier's does not mention, notably the focus of an earthquake in seismology and a focus of infection in medicine.
Written for this edition, 2026.