OBJECTIVES AND OCULARS 17 



The shortest violet rays producing the effect of light upon the 

 average normal human eye may be assumed to have a wave 

 length of approximately X 4000 (or 0.4 /x) 1 . It has been shown 

 that under ordinary conditions the smallest particle which will 

 be visible as a black spot upon a light ground must have a diam- 

 eter equal to at least half this value (Helmholtz-Abbe). More- 

 over, a lens, owing to diffraction, yields as an image of a point, 

 a diffraction disk and not a point. The final image may be con- 

 sidered as consisting of a series of diffraction disks or patterns, 

 and if the distances between bright points are such as to cause 

 an overlapping of the resulting disks or their surrounding circles, 

 a blurring of the image must result. Thus we are limited, in 

 our attempt to see and study infinitely small particles, by the 

 sensitiveness of the human eye, on the one hand, which cannot 

 properly respond to the stimuli of very short wave-lengths, and 

 to the fact, on the other hand, that no matter how great the 

 magnification employed we cannot bring about a separation of 

 the overlapping rings of the diffraction patterns. The result, 

 there fore, must be at the best a vague, blurred, uninterpretable 

 image or merely a diffraction pattern. 



If, therefore, our wave theory of light is correct, the most 

 minute particle which we may hope to render distinctly visible 

 by our compound microscopes by transmitted light must have 

 dimensions of at least 0.2 n. It should not be inferred, however, 

 that the existence of particles many times smaller cannot be 

 indicated, for an invisible particle may yield a large diffraction 

 pattern, a phenomenon which makes ultra-microscopic investi- 

 gations possible; but we must bear in mind that in the case of 

 ultra-microscopic particles we have no picture or image of their 

 shape or structure and that we know of their existence simply 

 through the light diffracted by them and thus have passed far 

 beyond the range of the resolving power of our lenses. Although 

 it is true that the limit of resolving power, 0.2^, has been seri- 

 ously questioned by men of recognized authority, it may be 

 accepted as beyond dispute that a moderately skillful micros- 



1 One micron, designated by the Greek letter M , is equivalent to one-thousandth 

 of a millimeter (0.001 mm.). 



