M. G. Quincke on the Refractive Index of the Metals. 433 



tion of the light reflected from these metals, as well as directly 

 from my researches on the displacement of the interference- 

 bands by means of thin metallic plates. 



At the same time, however, the theory of elliptical polariza- 

 tion, as developed by Cauchy, Beer, and F. Eisenlohr, leads to 

 this, that the refractive index of the metals, just like the ex- 

 tinction-coefficient, is a function of the angle of incidence ; and 

 indeed it follows that (see Phil. Mag. vol. xxvii. p. 169) 



„*=»« + sin 9 1,1 



7 2 =/-j-sin 2 IJ ■ ' W 



v and 7 being the refractive and extinction-coefficients for the 

 angle of incidence I, n and g being similarly related to the angle 

 of incidence 0°. 



The correctness of the first equation (4) may be shown by 

 using the interference-apparatus employed by me (described in 

 my former memoir (see vol. xxvii. p. 169), by observing the 

 displacement of the fringes of interference whilst the metallic 

 plate lying in the path of one of the interference-pencils of rays 

 is gradually inclined so that the angle of incidence of the inci- 

 dent rays gradually increases. 



As the inclination increases, the thickness of metal traversed 

 by the ray will increase, and consequently the displacement 

 produced thereby will also increase. On the other hand, how- 

 ever, the refractive index v will also be increased, and for a 

 certain angle of incidence rj, we shall have v=l when we have 

 ra<l. With an increasing angle of incidence, the displace- 

 ment will accordingly increase up to a certain extent, and then 

 again diminish. For a certain angle of incidence 77 the displace- 

 ment will be 0, and then we have, from equation (4), 



l = n 2 + s'm 2 r), \ . g > 



n=cosr). J " * ' 



Assuming the correctness of the theory, we have thus a 

 method of estimating n without knowing the thickness of the 

 plate. In this it is supposed that the displacement of the bands 

 of interference arising from the elliptical polarization of the light 

 passing through the metal is 0. 



If it be granted that the view propounded and supported by 

 me on former occasions* is correct, viz., that the rays polarized 

 perpendicular to the plane of incidence, and of which the vibra- 

 tions are perpendicular to the plane of incidence, suffer either 

 the same or no alteration at all of phase under all angles of 

 incidence, but that this is the case only with rays polarized 

 parallel to the plane of incidence, then it is only necessary to 



* Monatsbericht der Berliner Academie, Dec. 18, 1862, and March 16, 

 1863. 



Phil. Mag. S. 4. Vol. 27. No. 184. June 1864. 2 F 



