Of the Rays of Light. 175 
There are two circumstances which chiefly demand our attention in the case of re- 
flected light—namely: Ist, the amplitude of the vibration, on which the intensity of 
the light depends ; and 2dly, the phase. ‘The facts before us seem, toa certain extent, 
to bear on both these points. 
The reasonings of Fresnex with respect to the intensity of reflected light, are partly 
of an analogical nature, and very far 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 Fresnex has obtained for the in- 
tensity of reflected light has not received any direct confirmation from experiment, 
except in the case of a few observations made by M. Araco. It results from this for- 
mula that the intensity of the reflected light must be equal to that of the incident, or 
the whole of the light reflected, at the limiting incidence of 90°. Fresnev 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 cor- 
responding to this bar ; and as the intensity of the light in the dark bands is generally 
expressed by the formula (a—a’)’, we are forced to admit that a=a’, 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 vibration, there seems to 
be some uncertainty in the theory. The phenomena of thin plates compel us to ad- 
mit that half an undulation 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 con- 
siderations. ‘The light in the one case is reflected from the surface of a denser, in the 
other from that of ararer medium; and the mechanical laws, on which Fresnet 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 equivalent 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. Youne, indeed, who was the 
first to state this law, says expressly that where “light has been reflected at the sur- 
face of the rarer medium, it must be supposed to be retarded one-half of the appro- 
priate interval.” I cannot avoid thinking, however, that the very analogy by which 
he himself illustrates this point, and still more the reasonings of Fresnex on the sub- 
