LIMITS OF OPTICAL CAPACITY OP THE MICEOSCOPE. 417 



Let a be the point of convergence of rays, incident on h h'. 



— b re-union of rays refracted by k h'. 



— / the front principal focus. 



— y the back 



Further let 7i' represent the ratio of refractions of the mediam in 

 front of hh' 



n" represent the ratio of refractions of the medium 

 behind hh' 



a' the positive divergence -angle h'ah of the ray passing 

 in first medium through h' 



a the negative divergence-angle, in second medium 

 —h'hh 



/3' the magnitude of image aa" belonging to the rays 

 of the first medium. 



/3'' the magnitude of image — h'b" belonging to the 

 rays of the second medium. 



Firstly we have from similarity of triangles aa'c and hh"e 



(^' ae_^ 



13" ~ ch (1) 



Again, if we consider the short arc hh' of the refracting surface as 

 a straight line at right angles to the axis ah 



hh' = ah. tang, a' = — hh. tang, a" 



Or substitating the angles for the tangents which is allowable here 

 on account of the smallness of the angle : 



la" ah (2) 



Multiplying equations (1) and (2), we get 



__aV^ ^ ac. hh 



a . (3" , he. ah (3) 



