Refraction  of  Light  by  intensely  Opaque  Matter.         329 
Thus  in  a  certain  sense  R  cos  a  (that  is,  the  real  part  of  p)  may- 
be regarded  as  the  refractive  index  of  the  metal  for  the  kind  of 
light  under  consideration  ;  but  I  wish  to  remark  that  great  con- 
fusion has  arisen  in  the  use  of  the  expression  "  refractive  index  " 
as  applied  to  metallic  or  quasi- metallic  bodies,  the  same  name 
being  given  to  quantities  which,  though  coincident  for  transpa- 
rent matter,  may  here  differ  widely. 
Expressed  in  terms  of  <yl  and  h, 
^ 
R«M«-au/-x-,V1+3? 
or  if  ~yt  be  very  large, 
-r  „™         V       /   h     —  .    /  h 
ft  cos  a  =  —  a  /  — —  =  \  /  —^-) 
7v  V  2cD,      V  2Dc 
V= 
which,  we  have  seen,  presumably  increases  with  the  period  of 
vibration.  In  this  approximation  we  have  supposed  that  the 
influence  of  opacity  is  paramount,  so  that  sin  2a  =  —  1,  and 
R  cosa=—  Rsma  =  — t=« 
\/2 
The  wave-length  within  the  medium  may  be  taken  to  be 
on  substitution  of  the  value  of  c.  Hence,  if  h  be  constant,  the 
wave-length  in  the  metal  varies  as  the  square  root  of  the  wave- 
length in  air.  The  quantity  here  called  the  internal  wave-length 
is  that  which  physically  best  deserves  the  name ;  and  it  is  con- 
nected with  what  we  have  called  the  refractive  index  by  the 
usual  relation, 
Internal  wave-length  =  external  wave-length h- refractive  index; 
but  it  must  be  remembered  that,  from  an  analytical  point  of 
view   the  internal  wave-length  and  refractive  index  are  imagi- 
nary, being  denoted  by  \-—p  and  p,  respectively. 
The  factor  expressing  the  absorption  is 
€-R8inaaJ?_e-^R8iQa 
or,  in  terms  of  \f, 
2_^tana 
e     x' 
where,  it  will  be  remembered,  both  x  and  tan  a  are  negative, 
showing  that,  if  a  be  constant,  the  penetration  expressed  in  terms 
