For a microscope it will be simpler to proceed a little differently. The magnification increases as the object approaches the front of the objective lens. Suppose it is almost in contact. The waves from p (Fig. 24) reach o in the same phase, but those from q reach o more quickly through the upper half of the lens than through the lower half. Let the difference in the paths qao and qbo be l, that is, one of the light waves. Then there will be darkness at o so far as theFIG. 24 point q is concerned; i. e., the dark ring in the image of q will lie at o and will thus coincide with the bright center of the image of p. This condition of affairs corresponds to a displacement pq = ${\displaystyle \scriptstyle {\frac {1}{2}}}$l. Hence, if there were two luminous points at a distance pq = ${\displaystyle \scriptstyle {\frac {1}{2}}}$l apart, their diffraction images would overlap so as to be indistinguishable from each other. Hence ${\displaystyle \scriptstyle {\frac {1}{2}}}$l , or ${\displaystyle \scriptstyle {\frac {1}{100000}}}$ of an inch, is the "limit of resolution" in any microscope, as against ${\displaystyle \scriptstyle {\frac {1}{250}}}$ of an inch with the naked eye. So that here again the increase in accuracy is about four hundred times.

These theoretical deductions are amply confirmed by actual observation, and since in this investigation we have supposed a theoretically perfect lens, these results show that our present microscopes and telescopes, when operated under proper conditions, are almost perfect instruments.

Thus, Fig. 25 shows a micro-photograph of the specimen called Amphipleura pellucida, whose markings are about