# Page:Light waves and their uses.djvu/47

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Microscope, Telescope, Interferometer

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 visibleFIG. 23 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 angle is the angle subtended by r at the distance F, i. e., rF, and this, by the formula, is the same as the angle subtended by the light wave at the distance D—the diameter of the objective. This limiting angle for a five-inch lens would, therefore, be ${\displaystyle \scriptstyle {\frac {1}{250000}}}$ of an inch, i. e., about the size of a 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 ${\displaystyle \scriptstyle {\frac {1}{12500000}}}$ as against ${\displaystyle \scriptstyle {\frac {1}{2500}}}$ without the lens; i. e., the order of accuracy is increased about five hundred times.