OF THE RAYS OF LIGHT. 155 



expressly that where " light has been reflected at the surface of 

 the rarer medium, it must be supposed to be retarded one-half of 

 the appropriate interval." I cannot avoid thinking that the 

 very analogy by which he himself illustrates this point, and 

 still more the reasonings of Fresnel on the subject, lead to an 

 opposite conclusion, and tend to ascribe the effect which is found 

 to take place to reflexion at the surface of the denser medium. In 

 fact, it would appear from Fresnel's conclusions, that the sign of 

 the vibratory movement is in all cases changed by reflexion at the 

 surface of the denser medium, the angle of incidence exceeding the 

 polarizing angle ; and it can readily be shown that this change 

 of sign is equivalent to the addition of TT to the phase. 



The present case of interference seems to support this view. 

 It follows, as we have seen, from theory, that if the light under- 

 goes no change of phase by reflexion, the distances of the succes- 

 sive dark fringes from the edge of the shadow will be as the odd 

 numbers, 1, 3, 5, &c. ; so that the distance of the first dark band 

 from the edge will be half the interval between each succeeding 

 pair of dark bands. But it appears, on the contrary, from the 

 phenomena, that the distance is as far as the eye can judge 

 exactly equal to the succeeding intervals ; or that the bands are 

 all shifted from the edge by the amount of half an interval The 

 phenomena, therefore, require us to suppose that the phase of the 

 reflected wave is accelerated, and that the amount of this accele- 

 ration is exactly half a phase, or TT. For the general expression for 

 the shifting of the bands is ^X cotan a ; and as this is found to 

 be equal to A cotan a, it follows that /x = 1, or the acceleration 

 equal to TT. It appears then that when light is reflected at the 

 surface of a denser medium, the wave at the limiting incidence 

 at least gains half an undulation at the instant of reflexion. 



In order to satisfy myself more fully of the effects of reflexion 

 upon the phase, I repeated the experiment with polarized light. 

 The light was polarized, before it reached the aperture in the 

 screen, by transmission through a good tourmaline; and the 

 fringes were observed in various positions of the plane of polariza- 

 tion with respect to the plane of reflexion. I could detect 

 no sensible difference in the position of the fringes under all 

 these changes of circumstance ; and, in particular, the distance 

 of the first dark band from the edge of the shadow seemed, as 

 before, to be precisely equal to the intervals of the succeeding 



