JAMIN ON METALLIC REFLEXION- 69 



Thus we shall polarize the light successively in the plane of 

 incidence, and the plane perpendicular to it ; and in order to 

 obtain the proportion of light reflected in each of these two cases 

 by the metallic mirror, we shall turn the analyser until two 

 images of contrary name, produced by the two substances, be- 

 come equal : we shall find by two distinct observations, which 

 ought to agree, the azimuths (/3) and 90°— /3, of the principal 

 section; and the intensity of the hght reflected by the metal 

 will be equal to that reflected by the glass multiplied by the 

 square of the tangent of (/3). 



This method, which in a theoretical point of view is of extreme 

 simplicity, cannot lead to accurate results unless the index of 

 refraction of glass is perfectly known ; since the intensities 1'^ 

 and J'^ of the hght reflected by this substance are functions of 

 the incidence and of the index of refraction. Now there are two 

 methods of ascertaining this latter quantity : the first consists 

 in seeking directly for the index by forming the glass into a 

 prism ; the second in determining the angle of polarization (i) 

 of glass, and putting tan {i) =n. Unfortunately, the two methods 

 have given results differing by a notable quantity ; and in order 

 to choose between the two, it must be remembered that the pre- 

 ceding formulae cannot be used unless they are true in each par- 

 ticular case, and provided they give the intensity nothing for 

 light reflected at the angle of maximum polarization, when the 

 ray is polarized perpendiculaily to the plane of incidence, which 

 requires that we have tan {i)=n. We must therefore employ for 

 the determination of the index {n), a method which verifies for- 

 mulae (!•); I have adopted the following. 



The two formulae (1.) lead to a third, which gives us the value 

 of the azimuth A' of the reflected light, when the incident ray 

 is polarized at 45° to the plane of incidence ; this formula is the 

 following : 



tanA'=^"^;j + t 

 cos(l — r) 



a relation evidently verified by the same value of (n) as the pre- 

 ceding, since it is a consequence of them ; and instead of the 

 value of the index of refraction, which satisfies the former, we 

 may determine that which agrees with the last. We obtain suc- 

 cessively 



