Interference Bands formed by Rays at Small Angles. 197 



respectively AC + CB in air, and /x AD in glass. The difference in their 

 length is easily shown to be equal to 2yy. 



Let the surfaces be viewed from a point E at a distance L from X ; then, 

 noting that OEB = e, and writing B for /x cos /'o, it will be found that 

 T = ^(2X//iL), and that, consequently, the relative retardation of the 

 interfering rays is 2«BXv/(2£t7yu.L). 



Takiug into account the half -wave-length change of phase at the internal 

 reflection at B, the bands are bright or dark, according as the retardation is 

 nX or J (2/1 -F 



so that their spacing is not uniform. 



These bands differ in several other ways from those formed by normal, or 

 nearly normal, incidence. The latter practically have an objective existence 

 at the surfaces of interference, and can be viewed by a telescope adjusted to 

 focus an object at the distance of the plate from the observer, the reason 

 being that the size and position of the bands change only slowly with the 

 angle of incidence. In the case at present under consideration this condition 

 does not hold. As Stokes* puts it :— 



" When the angle of incidence becomes nearly equal to that of total 

 reflection, 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 surface 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 reflection, 

 the author used a piece of blackened paper, in which a small hole was 

 pierced with the point of a needle.'"' 



Stokes is here speaking of Newton's rings. In the case of bands between 

 flat plates, the aperture of the pupil need not be limited, if the observation be 

 made at a distance of some feet. 



Another peculiarity of these bands may be mentioned. When formed 

 by white light, the bands are, of course, coloured. For those distant from 

 the line of total reflection the blue is on the inside, i.e., nearest to that 

 line, but, for the band close to the line, the blue is on the outside. 

 Between them occurs a band which appears achromatic. The explanation is 



Hence 



for the dark bands 



* Stokes, ' Collected Papers,' vol. 2, p. 359, from 'B.A. Report,' 1850. 



