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Conjugate focus
(gcide) | Focus \Fo"cus\ (f[=o]"k[u^]s), n.; pl. E. Focuses
(f[=o]"k[u^]s*[e^]z), L. Foci (f[=o]"s[imac]). [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.
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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.
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Note: 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.
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3. A central point; a point of concentration.
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Aplanatic focus. (Opt.) See under Aplanatic.
Conjugate focus (Opt.), the focus for rays which have a
sensible divergence, as from a near object; -- so called
because the positions of the object and its image are
interchangeable.
Focus tube (Phys.), a vacuum tube for R[oe]ntgen rays in
which the cathode rays are focused upon the anticathode,
for intensifying the effect.
Principal focus, or Solar focus (Opt.), the focus for
parallel rays.
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Conjugate focus
(gcide) | Conjugate \Con"ju*gate\, a. [L. conjugatus, p. p. or conjugare
to unite; con- + jugare to join, yoke, marry, jugum yoke;
akin to jungere to join. See Join.]
1. United in pairs; yoked together; coupled.
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2. (Bot.) In single pairs; coupled.
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3. (Chem.) Containing two or more compounds or radicals
supposed to act the part of a single one. [R.]
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4. (Gram.) Agreeing in derivation and radical signification;
-- said of words.
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5. (Math.) Presenting themselves simultaneously and having
reciprocal properties; -- frequently used in pure and
applied mathematics with reference to two quantities,
points, lines, axes, curves, etc.
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Conjugate axis of a hyperbola (Math.), the line through the
center of the curve, perpendicular to the line through the
two foci.
Conjugate diameters (Conic Sections), two diameters of an
ellipse or hyperbola such that each bisects all chords
drawn parallel to the other.
Conjugate focus (Opt.) See under Focus.
Conjugate mirrors (Optics), two mirrors so placed that rays
from the focus of one are received at the focus of the
other, especially two concave mirrors so placed that rays
proceeding from the principal focus of one and reflected
in a parallel beam are received upon the other and brought
to the principal focus.
Conjugate point (Geom.), an acnode. See Acnode, and
Double point.
Self-conjugate triangle (Conic Sections), a triangle each
of whose vertices is the pole of the opposite side with
reference to a conic.
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