208 



PROGRESS IN MICROSCOPY 



6 is readily connected to the sphere radius. Let OA = x (Fig. 7.37) 

 then: 



tan d 



X 



whence: 



]Xr^—x^) 

 2d{n'-ii)x 



(7.22) 



] (r2-.T2) • 



The observed shift d = Ka is, in this case, actual as the difference 

 path varies continuously from the centre of the sphere. The previous 



Fig. 7.37. Fringes aspect in the spherule. 



formula does not apply, of course, to the edge of the sphere. Granting 

 m = x/r then, 



11 = 7? 



2dm 



(7.23) 



There is no need therefore to measure the radius /• of the sphere in 

 order to determine the index //: merely knowing ni = .v/r, i.e. the 

 distance OA = .v from the point the path difference is measured, is 

 enough. Jn Fig. 7.37, K is virtually -- 4/3 and OA - .v - 2/73, there- 

 fore m = 2/3 and: 



3d ' 



n = 11 



(7.24) 



