Corrections in a Newton' s-rings System. 



503 



into convenient form the more important of the above- 

 mentioned corrections. 



In the analysis here given a different course is followed. 

 Whilst only attempting to provide a first approximation, it 

 is hoped that it will show clearly the conditions under which 

 the parallel-plate formulae can be used, and the magnitude 

 of the correction to be applied in the cases of practical im- 

 portance where the use of the parallel-plate formulae is not 

 legitimate. 



Suppose, then, that we have a plano-convex lens resting' 

 on a plane reflecting surface. The central assumption 

 usually made is that <£, the angle of incidence of the light 

 on the lower reflecting surface, is, to the first order, the same 

 as the angle of incidence i of the light on the upper plane 

 surface of the lens, In which case the well-known relation 



2 fie cos i = n\ (i.) 



gives at once for the radius x of the n\h dark ring 



a 2 = Jln\ secz. 



For our purpose, it will be sufficiently exact to determine 

 (f> as a function of ?', and to substitute the value of cos <£ so 

 obtained in the equation 



2/jue cos (j) = n\. 



Fig. 2. 



Two cases are of special interest. 



Taking rectangular axes as shown (fig. 2), let light be incident 

 at an angle i on the upper surface of the lens in a plane 



