CH. /] 



MICROSCOPE AND ACCESSORIES 



<S 4. Optical Center. — The optical center of a lens is the point through 

 "which rays pass without angular deviation, that is, the emergent ray is parallel 

 to the 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 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 

 <:an be satisfied only by using the radius of the curved surface which is contin- 

 uous with the axis of the lens, then any line at right angles to the plane sur- 

 face 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 surface 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 peri- 

 pheral 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. 



\ 5. 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 



Figs. 10, 11. — Sectional views of 

 ■a concave or diverging and a convex 

 or converging lens to show that in the 

 concave lens the principal focus is vir- 

 tual as indicated by the dotted lines, 

 while with the convex lens the focus 

 is real and on the side of the lens oppo- 

 site to that from which the light 

 comes. 



deviation for rays traversing the center of the lens, there would be lateral dis- 

 placement. This is shown in Fig. 64 illustrating the effect of the cover-glass. 



\ 6. Secondary Axis. — Every ray traversing the center of the lens, 

 except the principal axis, is a secondary axis ; and every secondary axis is 



