CH. /.] 



MICROSCOPE AND ACCESSORIES. 



within the lens ; in 6-7 it is at the curved surface, and in the meniscus (8, 9) it is 

 wholly outside the lens, being situated on the side of the greater curvature. 



In determining the center in a lens with a plane surface, the conditions can be 

 satisfied only by using the radius of the curved surface which is continuous with 

 the axis of the lens, then any line at right angles to the plane surface will be par- 

 allel with it, and may be considered part of the radius of the plane surface. (That 

 is, a plane surface may be considered part of a sphere with infinite radius, hence 

 any line meeting the plane surface at right angles may be considered as the 

 peripheral part of the radius.) In Figs. 6, 7, (r') is the radius of the curved sur- 

 face and (r) of the plane surface ; and the point where a line joining the ends of 

 these radii crosses the axis is at the curved surface in each case. 



By a study of Fig. 4 it will be seen that if tangents be drawn at the peripheral 

 ends of the parallel radii, the tangents will also be parallel and a ray incident at one 

 tangential point and traversing the lens and emerging at the other tangential point 

 acts as if traversing, and is practically traversing a piece of glass which has paral- 

 lel sides at the point of incidence and emergence, therefore the emergent ray will 

 be parallel with the incident ray. This is true of all rays traversing the center of 

 the lens. 



\ 5. Secondary Axis. — Every ray traversing the center of the lens, except the 

 principal axis, is a secondary axis ; and every secondary axis is more or less oblique 

 to the principal axis. In Fig. 14, line (2), is a secondary axis, and in Fig. 15, line 

 (1). See also Fig. 57. 



Figs, io, ii. — Sectional views of a con- 

 cave or diverging and a convex or con- 

 verging lens to show that in the concave 

 lens the principal focus is virtual as indi- 

 cated by the dotted lines, while with the 

 convex lens the focus is real and on the 

 side of the lens opposite to that from which 

 the light comes. The principal focal dis- 

 tance is the distance along the axis, from 

 the optical center to the principal focus 







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\ 6. Principal Focus. — This is the point where parallel rays traversing the lens 

 cross the axis ; and the distance from the focus to the center of the lens measured 

 along the axis is the Principal Focal Distance. In the diagrams, Fig. 10 is seen 

 to be a diverging lens and the rays cross the axis only by being projected back- 

 ward. Such a focus is said to be virtual, as it it has no real existence. In Fig. 11 

 the rays do cross the axis and the focus is said to be real. If the light came from 

 the opposite direction it would be seen that there is a principal focus on the other 

 side, that is there are two principal foci, one on each side of the lens. These two 

 foci are both principal foci ; and as there may be foci on secondary axes also, 

 each focus on a secondary axis has its conjugate. In the formation of images the 

 image is the conjugate of the object and conversely the object is the conjugate of 

 the image. 



