114 



THE INTERFEROMETRY OF 



sufficiently sharp for adjustment. If the lens first struck by light is convex 

 and the second concave, their focal distances f\ and/ 2 , respectively, and their 

 distances apart D, the focal power i/F of the combination used is 



since j\ =/ 2 =/. The position of the equivalent lens is d = DF/fi =/ 2 =/. D, d 

 are both measured from the second or concave lens to the convex lens, and D 

 would always be smaller than /. If the lens system is reversed, F remains 

 the same as before for the same D, the system being again convex, but d is 

 reversed. The equivalent lens again lies toward the convex side of the system. 

 In other words, the equivalent lens generally lies on the same side of the 

 doublet as the convex lens. 



In the actual experiment, however, the rays go through the lens system 

 twice. In this case it is perhaps best to compute the distances directly. Of 

 the two adjustments, the one with the concave lens toward the grating and 

 the convex lens toward the mirror has much the greater range of focus relative 

 to the displacement D. Supposing the mirror appreciably in contact with a 

 convex lens, therefore, if & is its principal focal distance measured from the 

 concave lens, b-\-D = M its principal focal distance from the convex lens or 

 mirror, 



i = 2 // 2 - !/(/:+>) i 



b I -D( 2 /f z -i/(f l +D)) fi 



(2) 



where f\ is the (numerical) focal distance of the concave and /" 2 that of the 

 convex lens. If we now write 



(3) 6 = 5(i-D( 2 // 1 - 



equation (2) is easily converted into 



h fl />/2 



so that the usual value of the principal focal distance has been halved rela- 

 tively to the new position of the equivalent lens. If, as in the present case, 



fl =/2 =/ 



b = 



f f 2 - 

 f+D 



The following table shows roughly the corresponding values of D and M in 

 centimeters : 



