Refraction  of  Light  by  intensely  Opaque  Matter,         333 
between  the  limits  1  and  —7=.     Now  in  order  that  the  reflection 
^2 
may  be  perfect  at  all  angles  of  incidence,  it  is  only  necessary 
that  the  density  or  opacity  or  both  should  be  sufficiently  large ; 
and  then  cos  2/3  must  be  sensibly  equal  to  zero.  And  yet  if  the 
formula?  under  consideration  were  true,  there  would  always  be  a 
certain  angle  of  incidence  making  the  ratio  of  the  two  polarized 
components  very  different  from  unity — a  state  of  things  incom- 
patible with  a  nearly  complete  reflection.  I  do  not  think  that 
the  failure  of  the  formulae  for  light  vibrating  in  the  plane  of  in- 
cidence need  cause  surprise,  when  it  is  considered  that  FresneFs 
tangent-formula,  which  forms  the  starting-point  of  the  investi- 
gation, is  not  verified  even  with  transparent  media,  and  differs 
more  and  more  from  the  truth  as  the  refracting-power  increases. 
The  failure  of  theory  is  the  more  unfortunate,  because  the  rela- 
tive change  of  phase  and  ratio  of  amplitudes  for  the  two  polarized 
components  are  precisely  the  quantities  best  adapted  to  experi- 
mental measurement.  As  it  is,  we  must  conclude,  I  fear,  that 
the  careful  investigations  of  Jamin  on  the  subject  are  at  present 
unavailable  for  the  purpose  of  forming  an  estimate  of  the  values 
of  the  density  and  opacity  of  the  various  metals.  Experiments 
on  the  absolute  reflecting-power  of  the  metals  for  the  different 
parts  of  the  spectrum  at  perpendicular  incidence  would  be  va- 
luable and  probably  easy ;  but  they  do  not  appear  to  have  been 
attempted. 
It  has  hitherto  been  supposed  that  there  is  no  interruption  in 
the  continuity  of  the  metallic  medium  within  such  a  distance  from 
the  surface  that  the  intromitted  wave  is  still  sensible.  This  is  a 
very  different  thing  from  assuming,  as  it  has  been  asserted  that 
the  theory  does*,  that  the  reflection  takes  place  entirely  from 
the  surface,  if  indeed  such  an  assumption  could  have  any  mean- 
ing. When,  as  in  the  experiments  of  Quincke,  the  metallic 
layer  is  so  thin  as  to  transmit  a  sensible  quantity  of  light,  it  is 
clear  that  the  theory  requires  modification.  If  the  medium  on 
the  two  sides  of  the  metal  are  optically  similar,  a  sufficient  re- 
duction of  the  thickness  of  the  layer  must  at  last  result  in  a 
destruction  of  the  reflection,  just  as  with  thin  transparent  plates. 
One  of  the  most  remarkable  of  Quincke's  results  relates  to  the 
influence  of  a  thin  metallic  layer  on  the  phase  of  the  transmitted 
light.  In  many  cases  the  phase  was  accelerated  so  as  to  be  in 
advance  of  what  would  correspond  to  a  layer  of  air  in  place  of 
the  silver — an  effect  which,  according  to  ordinary  ideas,  would 
imply  a  refractive  index  less  than  unity.  However,  it  is  not  dif- 
ficult to  see  that,  in  regard  to  the  effect  on  the  phase  of  the 
*  Wullner,  Lehrbuch  der  Experimentale  Physik,  vol.  ii.  p.  471. 
