TRANSACTIONS OF THE SECTIONS. 19 
On the mode of Disappearance of Newton's Rings in passing the angle of total 
Internal Reflexion. By Professor Sroxes, M.A. “534 
When Newton’s rings are formed between the under surface of a prism and the 
upper surface of a lens, there is no difficulty in increasing the angle of incidence so 
as to pass through the angle of total internal reflexion. When the rings are ob- 
served with the naked eye in the ordinary way, they appear to break in the upper 
part on approaching the angle of total internal reflexion, and pass nearly into semi- 
circles when that angle is reached, the upper edges of the semicircles, which are in all 
cases indistinct, being slightly turned outwards when the curvature of the lens is small. 
The cause of the indistinctness will be evident from the following considerations. 
The order of the ring (a term here used to denote a number not necessarily integral) 
to which a ray reflected at a given obliquity from a given point of the thin plate of 
air belongs, depends partly on the obliquity and partly on the thickness of the plate 
at that point. When the angle of incidence is small, or even moderately large, the 
rings would not be seen, or at most would be seen very indistinctly, if the glasses 
were held near the eye, and the eye were adapted to distinct vision of distant objects, 
because in that case the rays brought to a focus at a given point of the retina would 
correspond toa pencil reflected at a given obliquity from an area of the plate of air, 
the size of which would correspond to the pupil of the eye; and the order of the rays 
reflected from this area would vary so much in passing from the point of contact 
outwards that the rings would be altogether confused. When, however, as in the 
usual mode of observation, the eye is adapted to distinct vision of an object at the 
distance of the plate of air, the rings are seen distinctly, because in this case the rays 
proceeding from a given point of the plate of air, and entering the pupil of the eye, 
are brought to a focus on the retina, and the variation in the obliquity of the rays 
forming this pencil is so small that it may be neglected. 
When, however, the angle of incidence becomes nearly equal to that of total in- 
ternal reflexion, a small change of obliquity produces a great change in the order of 
the ring to which the reflected ray belongs, and therefore the rings are indistinct to an 
eye adapted to distinct vision of the surfaces of the glass. They are also indistinct, 
for the same reason as before, if the eye be adapted to distinct vision of distant objects. 
To see distinctly the rings in the neighbourhood of the angle of total internal re- 
flexion, the author used a piece of blackened paper in which a small hole was pierced 
with the point of a needle. When the rings were viewed through the needle-hole, 
in the light of a spirit-lamp, the appearance was very remarkable. The first dark 
band seen within the bright portion of the field of view where the light suffered total 
internal reflexion was somewhat bow-shaped towards the point of contact, the next 
still more so, and so on, until at last one of the bands made a great bend and passed 
under the point of contact and the rings which surrounded it, the next band passing 
under it, and so on. As the incidence was gradually increased, the outermost ring 
united with the bow-shaped band next above it, forming for an instant a curve with 
a loop and two infinite branches, or at least branches which ran out of the field of 
view: then the loop broke, and the curve passed into a bulging band similar to that 
which had previously surrounded the rings. In this manner the rings, one after 
another, joined the corresponding bands till all had disappeared, and nothing was 
left but a system of bands which had passed completely below the point of contact, 
and the central black spot which remained isolated in the bright field where the light 
suffered total internal reflexion. Corresponding appearances were seen with day- 
light or candlelight, but in these cases the bands were of course coloured, and not 
_ near so many could be seen at a time. 
On Metallic Reflexion. By Professor StoxKes, M.A. 
The effect which is produced on plane-polarized light by reflexion at the sur- 
face of a metal, shows that if the incident light be supposed to be decomposed into 
two streams, polarized in and perpendicularly to the plane of reflexion respectively, 
the phases as well as the intensities of the two streams are differently affected by the 
reflexion, It remains a question whether the phase of vibration of the stream po- 
Jarized in the plane of reflexion is accelerated or retarded relatively to that of the 
name polarized perpendicularly to the plane of reflexion. This question was first 
¢ ided by the Astronomer Royal, by means of a phenomenon relating to Newton’s 
: c2 
