Diffraction  Theory  of  Microscopic  Vision.  159 
term,  or  central  beam,  the  illumination  in  the  focal  plane  is 
uniform  and  no  image  of  the  lines  of  the  grating  is  formed. 
If  the  first  spectrum,  i.  e.  the  first  periodic  term  in  (2) ,  is 
transmitted  by  the  lens,  an  image  is  formed  having  a  periodic 
structure  corresponding  to  that  of  the  grating,  but  in  which 
the  lines  are  much  blurred.  In  paragraph  4  it  was  shown 
that  an  actual  grating  may  be  considered  to  be  composed  of 
an  imperfectly  transparent  surface  on  which  are  superposed 
a  number  of  simple  gratings  each  of  which  is  responsible  for 
the  whole  of  the  light  in  the  spectra  of  one  order.  The  structure 
of  the  image  can  now  be  readily  explained.  The  lens  can,  so 
to  speak,  image  only  what  it  sees  ;  if  the  aperture  is  so  narrow 
that  it  does  not  gather  in  the  spectra  of  the  second  and  higher 
orders,  it  receives  no  light  from  any  of  the  simple  component 
gratings  except  the  first  one,  and  hence  can  only  image  that 
one.  Hence  the  image  will  represent  a  simple  grating- 
superposed  on  an  imperfectly  transparent  plate  and  will 
present  precisely  the  structure  indicated  in  fig.  3.  When 
the  aperture  of  the  lens  is  further  widened  so  as  to  admit 
spectra  of  higher  and  higher  orders,  the  definition  becomes 
sharper  and  sharper  and  the  image  in  general  approximates 
more  and  more  closely  to  a  true  representation  of  the  object, 
but  with  exceptions  which  will  be  mentioned  in  paragraph  9. 
These  results  may  be  readily  verified  with  an  ordinary 
microscope  if  central  illumination  is  used  and  an  iris  diaphragm 
is  placed  above  the  objective  for  conveniently  varying  the 
aperture  ;  the  diffraction  spectra  can  be  seen  by  removing 
the  eyepiece  and  looking  down  the  tube,  and  the  iris  can  then 
be  adjusted  to  intercept  all  spectra  above  those  of  a  given 
order.  The  effects  are  best  studied  with  monochromatic 
illumination.  The  shaded  grating  mentioned  in  paragraph  5 
is  a  particularly  interesting  object  to  examine  ;  when  the  iris 
is  wide  open,  the  lines  are  seen  to  be  considerably  sharper 
near  one  edge  of  the  grating  than  near  the  other,  but  when 
the  iris  is  contracted  so  as  to  transmit  only  the  spectra  of  the 
first  order,  the  lines  appear  equally  blurred  over  all  parts  of 
the  plate. 
7.  A  orating  ruled  with  lines  closer  together  than  the  wave- 
length  of  light  gives  no  spectra  with  central  illumination  and, 
if  the  lines  are  closer  together  than  half  a  wave-length,  no 
spectra  will  be  given  under  any  circumstances.  As  Abbe 
has  shown,  this  sets  a  limit  to  the  possible  resolving  power  of 
the  microscope;  for  the  lines  are  imaged  by  the  diffracted 
light,  and  when  none  is  diffracted  no  image  of  the  lines  can  be 
formed.  If  green  light  is  used  to  illuminate  the  object,  the 
limit  of  possible  resolution  will  be  reached  at  about  40,000 
