328  The  Hon.  J.  W.  Strutt  on  the  Reflection  and 
These  are  Cauchy's  formulae  for  light  polarized  in  the  plane 
of  incidence.     At  perpendicular  incidence, 
0=0,     #,=(),     c  =  l,     u=0, 
whence 
tan/=  2IUo^  =  2^T«  VR  +  R/' 
which  may  be  expressed  in  terms  of  y,  and  h  by  means  of : — 
ry2  V2       ^ 
R2  cos  2«  =  -4 ;   R2  sin 2«  =  -  -S  -^r- 
In  the  case  of  metal  the  reflected  light  is  a  large  percentage, 
and  therefore  tan/  is  considerable.     This  can  only  be  when  R 
-is  great ;  and  then  ^  is  relatively  very  small.     Approximately 
therefore 
tan/= 
R  7  'V    -  '   c2p; 
V  X  +  ^ 
or,  if  -yr-  is  considerable, 
2cosa        \/2.7,       A  /       '     A2     ' 
7/       VD' 
c2D,2      7/V    2cD, 
Also 
and  thus,  when  the  opacity  is  so  great  that  the  reflected  light 
is  a  large  fraction  of  the  whole,  its  intensity  will  be 
\/h+s/ZDc 
If  we  suppose  that  h  is  constant  for  the  different  waves  of  light, 
we  find  that  the  reflection  is  better  and  better  the  longer  the 
wave,  since  c  varies  inversely  as  the  period  of  vibration.  Most 
metals,  it  would  appear,  reflect  the  red  rays  in  greater  quantity 
than  the  more  refrangible,  and  dark  heat  better  than  any. 
The  wave  entering  the  metal  is  represented  by  fiet'<°'*+c*),  or, 
on  substitution  of  its  value  for  ap 
fcc— Rsinaar     gi(R  cos  uax+ct) 
C  C 
The  velocity  of  wave-propagation  is  ^ — - —  against  -  in  air. 
