1916] on Problems in Capillarity 809 



Colour A^ariations. 



The colours shown by liquid films are the index of their thickness, 

 becoming especially definite as the greatest tenuity is reached. The 

 limit in this direction is the so-called black film, by which is meant 

 a film too thin to cause colour by interference. 



A liquid film has two reflecting surfaces, so that the light coming 

 from the film is due to* reflection from the upper and the lower 

 surface. This latter portion will have travelled a slightly longer 

 path than the first, and in a denser medium, where its velocity is 

 lower. The vibrations will thus emerge out of step or beat with the 

 part reflected at the upper surface, which has travelled only in air, 

 and interference between the two portions must follow. This will 

 depend in amount on the length of the path in the liquid, that is, 

 on the thickness of the liquid film and the inclination of the path 

 of the light to the reflecting surfaces. When the film becomes very 

 thin, the length of this path in the liquid approaches the order of 

 a few wave lengths of light, and the interference eff'ect will then 

 become appreciable. If the light be monochromatic, that is, com- 

 posed of one wave length only, alternate light and dark bands will 

 be seen varying in character w^ith the specific monochromatic light. 

 When composite light is used, as in the case of ordinary white light, 

 various wave lengths will be successively suppressed as the thickness 

 of the film decreases, and the reflected light being deprived of these 

 will accordingly appear coloured. 



The limiting case of the '* black " film is obtained when the 

 thickness of the film is very small compared to the wave length of 

 ordinary light ; no sensible interference can then be caused in the 

 film because of the extreme shortness of the path therein. However, 

 all the rays that have been reflected in the liquid — i.e., from the lower 

 surface — sufi'er no modification ; those which are reflected on the 

 liquid are retarded or held back half a beat, and will thus be com- 

 pletely out of step Avith those coming out from the lower surface, 

 with the result that an apparent blackness results. Such feeble 

 light as there is appears neutral and faint on a dark ground, and 

 represents, so to speak, no more than the difference in general 

 intensity suffered by the internally reflected light, due to the slight 

 absorption in the film. 



In the same way the light passing through the film becomes 

 coloured. The two portions now producing colour by interference 

 may be regarded, on the one hand, as that which has simply been 

 bent or refracted slightly in passing through the film ; and, on the 

 other hand, as that which instead of passing straight through is 

 reflected up from the lower surface and down again from the upper 

 sm-face before following the course of the unreflected beam. The 

 amount of retardation in the film is the same as was the case between 

 the two reflected portions of light previously considered. But none 



