22 ELEMENTARY PRINCIPLES OF MICROSCOPICAL OPTICS 



Also, if x is the distance of a focus from F, the principal focus, 

 and y, the distance of its conjugate from F', the other principal 

 focus on the other side, then 



or, 



In an equiconvex lens of crown glass if /u = l'5, F= radius of 

 curvature. But in a plano-convex lens of crown glass if ^ = 1 > 5, 

 F= twice the radius of curvature. 



In the above formula the thickness of the lens has been neglected. 

 In thick lenses, however, its effect must not be disregarded, even if 

 only approximate results are required. A very approximate deter- 

 mination of the principal focal length of an equiconvex lens measured 

 from the surface may be made by subtracting from the result 

 obtained by the foregoing formulae one-sixth of the thickness of the 

 lens. (See fig. 25.) 



Examples. Equiconvex lens of crown glass /u=l'5, r=^, thick- 

 ness=J. By above formula F=^. Subtracting from this one- 

 sixth of the thickness of the lens, we get F=^ as the distance 

 between the focus and the surface of the lens. This is only -^l^ inch 

 from the truth. If the lens were a sphere it would be necessary to 

 subtract J of its thickness. 



In the case of a plano-convex lens the principal focus on the 

 convex side is equal to twice the radius as above, but on the plane 

 side two-thirds of the thickness of the lens must be subtracted from 

 it. 



In a hemispherical lens of crown gla-ss ^ = 1'5, radius =]>, thick - 

 ness=^, the principal focus on the convex side will be one inch 

 from the curved surface and on the plane side inch from the plane 

 surface. 



In an equiconcave lens the foci are virtual and are crossed over ; 

 thus, the lens in fig. 25 A is equiconcave, the focus F, instead of being 

 measured from A to the right hand, must be measured to the left 

 hand; consequently, f of the thickness must be subtracted from 

 the focal length in order to determine the distance of F from the 

 surface of the lens. 



A plano-concave lens follows the plano-convex, but the foci are 

 virtual and crossed over. From the principal focus on the curved 

 side subtract | of the thickness, and from that on the plane side 

 subtract the whole thickness of the lens. 



Examples. Equiconcave of dense flint /x = l'75, radius = ^, 

 thickness J, F by formula = ; subtract from this } of the thick- 

 ness of the lens, we obtain |,' which is only 1 -J ir inch too short. 



Plano-concave of dense flint /* = 1*75, radius= J, thickness J, 

 F by formula= - f , subtract from this the thickness of the lens. 

 Then F= -^ ; this is the focal distance from the plane side. For 

 the focal distance from the curved side subtract f of the thickness, 

 then F= (; , which is ^ inch too long. 



The pi*incipal focus of a combination of two or more lenses, whose 



