68 JAMIN ON METALLIC REFLEXION. 



reflect from the middle of this double plate a ray polarized in 

 the plane of incidence : one half of the ray will be reflected by 

 the glass, the other by the metal ; both will remain polarized in 

 the azimuth of 0^, and will give only a single image in traversing 

 a doubly-refracting prism, whose principal section coincides with 

 the primitive plane of polarization. 



But if we turn this prism through an angle (/S), we shall ob- 

 tain one ordinary and one extraordinary image for each of the 

 two portions of the beam reflected by the glass and by the metal : 

 hence there will be four images, whose intensities will be — 



Metal. Glass. 



O J2cos2/3 J'2cos2/3 



E J2sin2/3 J'2sin2,3. 



When (jS) varies, the ordinary and extraordinary images un- 

 dergo inverse changes of intensity ; and there is always a parti- 

 cular value of ((3) which makes the oi'dinary image of the metal 

 equal to the extraordinary one of the glass. 

 We have in this case, 



J2cos2/3 = J'2sin2/3; 

 and replacing J'^ by its value given by Fresnel's formulae, 



P=tan^/3S5l|i::i^; (2.) 



'^sm2(l+r) ^ ' 



If, on the contrary, we seek for the value (/3') which makes 

 the extraordinary image of the metal equal to the ordinary one 

 of the glass, we obtain 



P = cot^/3'^Jjl^^ (3.) 



Experiment will give us the values of (/3) and (/3'), which ought 

 to be complementary, and we shall calculate J^ by means of the 

 formulae (2.) and (3.). 



It is moreover obvious that this method is applicable to the 

 case where the light is polarized in the azimuth of 90° : the azi- 

 muth of equal tints will be determined in the same way, and we 

 shall obtain 



I.^tan^g tan^(l-^-) I'^^cot^ Qf^^^^^il^ . M^ 



'^"^ ^tan2(H-r)' "^ '^''^ ^ tan^(l +r) ' " ^^■> 



only, in the neighbourhood of the angle of polarization for glass, 

 there will no longer be any light reflected by this substance, and 

 therefore no comparison possible ; hence will result a gap of 

 some degrees in the experiment. 



