154: ON A NEW CASE OF INTERFERENCE 



indeed from being strictly demonstrative. Still, however, they 

 have led to conclusions fully borne out by experience, and of the 

 most interesting kind ; and we can hardly refuse our assent to 

 doctrines which bear with them such characters of truth. The 

 formula which Fresnel has obtained for the intensity of reflected 

 light has not received any direct confirmation from experiment, 

 except in the case of a few observations made by M. Arago. It 

 results from this formula that the intensity of the reflected light 

 must be equal to that of the incident, or the ichole of the light 

 reflected, at the limiting incidence of 90. Fresnel himself notices 

 this consequence, and adds that we should doubtless find it to 

 be experimentally true, if we could reach this limit. Now the 

 present experiment affords the means of examining this conclusion, 

 and seems fully to establish it. We have already alluded to the 

 intense blackness of the first dark bar, in the phenomena now 

 described. As far as the eye can judge, the intensity of the light 

 is absolutely nothing at the points corresponding to this bar ; and . 

 as the intensity of the light in the dark bands is generally ex- 

 pressed by the formula (a - a') 2 , we are forced to admit that a = d y 

 or that the intensities of the direct and reflected lights are equal 

 at this extreme incidence. 



With respect to the effect of reflexion upon the phase of vibra- 

 tion, there seems to be some uncertainty in the theory. The 

 phenomena of thin plates compel us to admit that half an undula- 

 tion is either lost or gained, by the wave reflected from the first or 

 second surface ; so that half an undulation must be added to, or 

 subtracted from, the difference in the lengths of the paths traversed 

 by the two waves. That such an effect should take place is in the 

 highest degree probable from theoretical considerations. The 

 light in the one case is reflected from the surface of a denser, in 

 the other from that of a rarer medium ; and the mechanical laws, 

 on which Fresnel has founded the doctrine of reflexion, lead us to 

 the conclusion that the displacements of the ethereal particles, in 

 the moment after reflexion, must be of opposite signs in the 

 two cases. This difference in the phase of the vibration is equi- 

 valent to a difference of half an undulation in the length of the 

 path. 



But it does not seem to be clearly understood to which surface 

 we are to attribute this physical change in the condition of the 

 ray. Dr. Young, indeed, who was the first to state this law, says. 



