684, 



4. Non-Uniform Films : Normal Incidence. 



When a mixed plate is held at some distance from the 

 eye between it and a source of light of small dimensions, 

 the film becomes visible by the light diffracted in passage 

 through it. Strictly speaking, it is not the whole film that 

 appears luminous, but only the laminar diffracting boundaries 

 in it or such portions of them as are effective in scattering 

 light in directions reaching the eye of the observer. Since, 

 as we have seen, the light scattered by each elementary 

 laminary boundary exhibits maxima and minima of intensity 

 in various directions depending only on the thickness of the 

 film, the appearance of the mixed plate should vary with 

 the direction in Avhich it is observed. This is actually the 

 case, and the effects observed are most striking with a non- 

 uniform film of graduated thickness formed between two 

 lenses of the kind used for observation of Newton's rings. 

 A film of this kind is very suitable for quantitative work in 

 testing the accuracy of formulae (1) and (2) given above, as 

 the value of t varies from point to point of the film in a 

 perfectly regular and determinable manner. Taking first 

 the case in which the film is observed very nearly in the 

 direction of the incident light, so that the angles of diffraction 

 are small, formulae (1) and (2) agree in showing that, for the 

 regions at which (/x— Y)t is an integral number of wave- 

 lengths, the diffracted light is of minimum intensity — that is, 

 the film as seen by the light scattered by it shows a succession 

 of black rings at these points. On altering the angle of 

 observation, the appearance of the film alters, and we have 

 now to consider separately the two sets of laminar boundaries 

 which diffract light to the observer's eye according to 

 formulae (1) and (2) respectively. From the graphs ex- 

 hibited in fig. 1 it is evident that these should behave 

 differently. Therefore, the rings seen on the film should 

 bifurcate, one set moving outwards, that is from the thinner 

 to the thicker part of the film, and the other set should move 

 inwards. For certain angles of diffraction the two sets 

 would be completely out of step, and this would result in a 

 blurred appearance of the film. At other positions they 

 would fall into step, and the dark and bright rings on the 

 film would again be conspicuous. 



. The foregoing indications of theory are in agreement with 

 what is actually observed. Owing to the finite area of the 

 film, the angle of observation is different for different portions 

 of its surface ; and as the eye is gradually moved outwards 

 away from the line of direct vision of the source, one or two 



