Fo*cim"e*ter (?), n. [Focus + -meter.] (Photog.) An assisting
instrument for focusing an object in or before a camera. Knight.
Fo"cus (?), n.; pl. E. Focuses (#), L. Foci (#). [L. focus hearth,
fireplace; perh. akin to E. bake. Cf. Curfew, Fuel, Fusil the firearm.]
1. (Opt.) A point in which the rays of light meet, after being
reflected or refracted, and at which the image is formed; as, the focus
of a lens or mirror.
2. (Geom.) A point so related to a conic section and certain straight
line called the directrix that the ratio of the distance between any
point of the curve and the focus to the distance of the same point from
the directrix is constant.
Thus, in the ellipse FGHKLM, A is the focus and CD the directrix, when
the ratios FA:FE, GA:GD, MA:MC, etc., are all equal. So in the
hyperbola, A is the focus and CD the directrix when the ratio HA:HK is
constant for all points of the curve; and in the parabola, A is the
focus and CD the directrix when the ratio BA:BC is constant. In the
ellipse this ratio is less than unity, in the parabola equal to unity,
and in the hyperbola greater than unity. The ellipse and hyperbola have
each two foci, and two corresponding directrixes, and the parabola has
one focus and one directrix. In the ellipse the sum of the two lines
from any point of the curve to the two foci is constant; that is:
AG+GB=AH+HB; and in the hyperbola the difference of the corresponding
lines is constant. The diameter which passes through the foci of the
ellipse is the major axis. The diameter which being produced passes
through the foci of the hyperbola is the transverse axis. The middle
point of the major or the transverse axis is the center of the curve.
Certain other curves, as the lemniscate and the Cartesian ovals, have
points called foci, possessing properties similar to those of the foci
of conic sections. In an ellipse, rays of light coming from one focus,
and reflected from the curve, proceed in lines directed toward the
other; in an hyperbola, in lines directed from the other; in a
parabola, rays from the focus, after reflection at the curve, proceed
in lines parallel to the axis. Thus rays from A in the ellipse are
reflected to B; rays from A in the hyperbola are reflected toward L and
M away from B.