STUDY OF ORES AND METALS. 413 



we put 



-=- = tan p' = tan xpe'''^ = tan \p{cos A + i sin A) 



RP _ _ _ _ (IQ) 



_ {Rsx Esi - R sjEs i) - {RsiEp 2 - R sjEp,) tan e ^^ 



~ {RpiEsi - RP2ES1) - {RpiEp2 - RpiEpi) tan e ' 

 in which tan e = Es/Ep and the azimuth angle 'A is real, then A is the rela- 

 tive phase difference of the components normal and parallel to the plane of 

 incidence. By equating the real and imaginary parts of this equation (o zero, 

 we obtain equations from which ^ and A can be computed. The equation 

 shows that for a certain angle of incidence the phase difference may be "'/a; 

 for this angle of incidence the reflected wave is plane-polarized. If e = 4S°, 

 then this angle of incidence, i, is called the principal angle of incidence and 

 the angle "^ the principal azimuth. From these two angles it is possible in 

 certain cases (especially isotropic bodies) to compute the refractive index 

 and the absorption index of the reflecting medium. Different methods have 

 been devised for ascertaining these angles ; practically all the methods avail- 

 able for ascertaining the refractive and absorption indices of absorbing sub- 

 stances are based on the above equations or certain modifications of the same, 

 deduced on the basis of simplifying assumptions. 



Vertical Incidence. 



In case the angle of incidence is zero, i = o, the above equations 

 reduce to the following : 



(r — «o2)(g^ — «ii)=«i2', (11') 



- q~ — ait ai2 , ,, 



tan 5 = "^ = =^ — , {12a') 



an r - «ii 



£cose — Rcosp= Di cosSi -|- Z)o cos 82, 

 £sine+ Rsmp= D^ s'mJ^-j- D^s'm^, (15', 15'^?) 

 q^E cos e -|- q,,R cos p = QiD.^ cos 8^ + ^2^2 cos 82. 

 q^E sin e — q„R sin p^^q^D^^ sin 8^ + q..D^ sin 80. 

 For uniradial azimuths we find for 8^, 

 ' Epi — Rp\ = cos 5i, 



Esi + ^^1 = sin 5i, 



5i 

 Epi + Rpi = — cos 5i, 

 2o 



?i • ~ 

 Esx — Rsi = — sin 5i. 

 go 



