MEASURING DRY MASSES WITH INTERFERENCE MICROSCOPES 221 



changing over from one fringe to the next, thickness increases or 

 decreases by A/2. This is no longer true if shifting the source moves 

 the images So and S'^ away from the axis. Nor is the beam perpendicular 

 any longer: its slant is a (Fig. 8.13). The inter-space fringe then 

 equates A/(2cosa). If a non-pinpoint source is now considered, 

 a system of fringes is correlated to every element of the source. 

 Inter-fringe spacing changes from one system to another. Finally, 

 owing to these phenomena adding up, two occurrences take place: 



(a) The fringe inter-space observed is no longer -^/2, thus giving 

 rise to errors in path-difference measurements; 



(b) Fringe contrast drops rapidly as path-difference increases. 



It may be taken for granted that the path differences considered 

 are always small enough so that fringe contrast does not drop sub- 

 stantially. For instance, an illuminating aperture sin a = 0-60 does 

 not materially affect contrast if the path difference does not exceed 

 approximately four wave-lengths (Dyson). 



Tolmon and Wood, Gates, Bruce and Thornton have investigated, 

 in reflecting objects, the effects of the angle a on fringe inter-spacing. 

 The relevant data are tabulated hereunder: 



The above table does not show the data corrections needed to 

 secure exact measurements. It evinces for every object exhibiting the 

 path difference d, the aperture a of the incident beam not to be exceeded 

 in order to attain a measuring accuracy within /'./lO, ^120 or A/ 100. 

 For instance, it is required to measure a reflecting object, whose 

 thickness e gives rise to a path difference d = 2e = 3A, within //1 00. 

 The illuminating aperture should be reduced to the value sina < 010. 

 As regards transparent objects, the path difference is {n — n')e in 

 normal incidence, and n and n' are then to be included in the cal- 

 culation. 



