30 Light Waves and Their Uses 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 Z, that is, one of the light waves. Then there will be darkness at o so far as the a b FIG. 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 = ?L Hence, if there were two luminous points at a distance pq = \l apart, their diffraction images would overlap so as to be indistinguishable from each other. Hence £Z, or in any microscope, as against ^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 | Microscope, Telescope, Interferometer 31 100,000 to the inch. This is about the theoretical limit for blue light. By using the portion of the spectrum beyond the violet it might be possible to go still farther. Doubtless by a much higher magnification a much more accurate setting on a given phase of the fringes could be made, and hence a corresponding increase of accuracy of measurement could be attained. But this involves a great loss of light, since the intensity varies inversely as the square of the magnification. Consequently, even with a threefold magnification the intensity is diminished ninefold, so that it would be difficult to see the image unless the illumi |