Quetelet's Rings and other Allied Phenomena. 839 

 light 



I=e~^($ -e- B <*N>, .... (6) 



where the constant B is determined by the structure of the 

 film. The remainder of the energy is scattered. 



We have thus analysed the disturbance when it has 

 entered the film into two portions : (a) a regularly-trans- 

 mitted portion of reduced intensity, and (6) a portion 

 scattered in various directions in a manner depending on 

 the structure of the film*. This complex disturbance is • 

 reflected from the silvered surface, and in passing out through 

 the film is again dealt with in the same way by it. Finally, 

 when the light emerges from the mirror, we have four types 

 of disturbance : (a) a regularly-transmitted wave, (6, a 

 scattered-transmitted disturbance, (c) a transmitted-scattered 

 disturbance, and (d) a twice-scattered disturbance. Of 

 these, (a) gives the geometrical reflected image of the source ; 

 (6) and (c) are in permanent phase-relation, and, being of 

 equal intensity, give interferences of maximum visibility ; 

 (d) appears as an overlying general illumination which 

 diminishes the visibility of the interferences due to (b) and 

 (c). The importance of (d) relatively to (b) and (c) depends 

 on the transmitting power of the film as defined by equation 

 (6), and also on the manner in which the energy of the 

 scattering light is distributed in different directions. A 

 relatively opaque film or a film that concentrates most of 

 the scattered light in a small solid angle, would give inter- 

 ferences of smaller visibility than a very transparent film 

 or a film that scatters through very wide angles. It can 

 easily be shown that in oblique transmission through the 

 film its transparency as determined by the phase-differences 

 in passage through it must decrease. Hence the visibility 

 of the interferences must decrease with increasing obliquity 

 of incidence. This is exactly what is observed. Further, 

 the improvement up to a certain stage in the visibility of 

 the interferences produced by interposing a liquid between 

 the rough surface and the mirror is also what is to be 

 expected on the present theory as the operative phase- 

 differences are diminished. 



* In regard to the distribution of energy in different directions in the 

 light scattered in passing through a heterogeneous medium, see N. K. 

 Sethi, Proc. Ind. Assoc, for the Cultivation of Science, vol. vi. parts 

 iii. & iv. p. 128 (1920). 



