conjugate focus

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 \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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