[CH. I 



MICROSCOPE AND ACCESSORIES 



incident ray. It is determined geometrically by drawing parallel radii of the 

 curved surfaces, r-r' in Figs. 4-9, and joining the peripheral ends of the radii. 

 The optical center is the point on the axis cut by the line joining the peripheral 

 ends of the parallel radii of the two lens surfaces. In Figs. 4-5 it is within the 

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

 side 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 parallel 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 

 parallel 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. 



Thick Lenses. — In all of the diagrams of lenses and the course of rays through 

 them in this book the lenses are treated as if they were infinitely thin. In thick 

 lenses like those figured, while there would be no angular deviation for rays trav- 

 ersing the center of the lens, there would be lateral displacement. This is shown 

 in Fig. 57 illustrating the effect of the cover-glass. 



\ 5. Secondary Axis. — Every raj- 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. 5S. 



Figs. 10, 11. — Sectional views of a 

 concave or diverging and a convex or 

 converging lens to show that in the con- 

 cave lens the principal focus is virtual as 

 indicated by the dotted lines, while with 

 the convex lens the focus is real and on 

 the side of the lefts opposite to that from 

 which the light comes. 



\ 6. Principal Focus. — This is the point where rays parallel with the axis and 

 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 pro- 

 jected backward. Such a focus is said to be virtual, as it has no real existence. In 



