Microscope, Telescope, Interferometer 29 In most cases these diffraction rings are so small that they escape notice, unless the air is unusually quiet and the lens exceptionally good. If these conditions are satisfied, and the instrument is focused on a very small or distant bright object (a star, or a pinhole in front of an electric arc), the rings are readily visible with a sufficiently high-power eye-piece. They may be much more readily observed, however, if the ratio of diameter to focal length be diminished by placing a circular aperture before the lens. The smaller the aperture, the larger will be the diffraction rings. Fig. 23 is a photograph of the phenomenon, showing the appearance of the rings when the diameter of a lens of five meters’ focal length has been reduced to one centimeter. In the case of a telescope the corresponding limiting T angle is the angle subtended by v at the distance F, ?. and this, by the formula, is the same as the angle subtended by the light wave at the distance I) — the diameter of the objective. This limiting angle for a five-inch lens would, therefore, be -g^oViro quarter of a dollar viewed at the distance of a mile. This could be measured to within one-fifth of its value, so that the accuracy of measurement in this case corresponds to TTToinro" | 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 |