156 ON A NEW CASE OF INTERFERENCE. 



bands, whether the light was polarized in the plane of incidence, 

 or in the plane perpendicular to it. 



This result seems to be just what might be expected from 

 Fresnel's theory of reflexion. From this theory it appears that if 

 + a be the coefficient of the displacement of the incident ray, or 

 the amplitude of the vibration, and t and f the angles of incidence 

 and refraction, the coefficients of displacement of the reflected ray 



will be 



sin (t - tan (i - ?} 



-a-^r. =, or +a 



_ x . , tan ( + i'} 



according as the plane of polarization coincides with the plane of 

 reflexion, or is perpendicular to it. Now the former quantity is 

 always negative, so long as i is greater than *', or the ray incident 

 on the surface of the denser medium. Under the same circum- 

 stances, the latter quantity is positive or negative, according as 

 i + i' is less or greater than 90, or the angle of incidence below or 

 above the polarizing angle. For very oblique reflexion, then, both 

 displacements are negative ; and, therefore, whether the plane of 

 polarization coincides with, or is perpendicular to the plane of 

 reflexion, the wave will undergo a change of half a phase at the 

 instant of reflexion. 



From Sir David Brewster's important researches on the nature 

 of metallic reflexion, it appears that a plane-polarized ray, which 

 is incident upon a metallic reflector, becomes elliptically-polarized 

 after reflexion ; a result which indicates a difference in the phases 

 of the two resolved vibrations. But it appears further, from the 

 same researches, that this difference of phase varies with the inci- 

 dence, and vanishes altogether at the extreme incidences ; so that 

 at the limiting incidence of 90, there is either no alteration in the 

 phase of vibration, whether parallel or perpendicular to the plane 

 of reflexion, or that alteration is the same for the two vibrations. 

 From some observation of the fringes produced by the interference 

 of direct light with that reflected from speculum metal, I conclude 

 that the former is the case. 



