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foci

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foci

 

  1  definition  found 
 
  From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]: 
 
  Focus  \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  refrcted,  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 
  distace  between  any  point  of  the  curve  and  the  focus  to 
  the  distance  of  the  same  point  from  the  directrix  is 
  constant. 
 
  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. 
 
  3.  A  central  point;  a  point  of  concentration. 
 
  {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,  or  Solar},  {focus}  (Opt.),  the  focus  for  parallel 
  rays.




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