Michelson A. A. Light waves and their uses (1903)

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In the last lecture it was shown that in many cases the interference fringes could be observed with a very large difference in path—a difference amounting to over 500,000 waves. It may be inferred from this that the wave length, during the transmission of 500,000 or more waves, has remained constant to this degree of accuracy; that is, the waves must be alike to within one part in 500,000. The idea at once suggests itself to use this invariable wave length as a standard of length. The proposition to make use of a light wave for this purpose is, I believe, due to Dr. Gould, who mentioned it some twenty-five years ago. The method proposed by him was to measure the angle of diffraction for some particular radiation — sodium light, for example—with a diffraction grating. If we suppose Fig. GO to represent, on an enormously magnified scale, the trace of such a grating, then the light for a particular wave length — say one of the sodium lines— which passes through one of the openings in a certain direction, as AB, is retarded, over that which passes through the next adjacent opening, by a constant difference of path; and therefore in the direction AB all the waves, even those which pass through the last of a very large number of such apertures, are in exactly the same phase. There will be then, if we are observing in a spectrum of the first order, as many waves in this distance AB as there are apertures in the distance AC. A diffraction grating is made by ruling upon a glass or a metal surface a great number of very fine lines by a ruling diamond, the number being recorded by the ruling-machine


Light Waves as Standards of Length


itself, so that there can be no error in determining the number of rulings. This number is usually very large, between 50,000 and 100,000. Since this number of lines is accurately known, we know also the number of spaces in the whole distance A C. This distance can be measured by comparing the two end rulings with an intermediate r

standard of length, which ^

has been compared with the standard yard or the standard meter with as high a degree of accuracy as is possible in mechanical measurements. If, now, we know also the angle ACB, we can calculate the distance AB; and since we know the number of waves in this distance, which is the same as the number of apertures, we have the means of measuring the length of one wave. It will be observed, in making such an absolute determination of wave length by this means, that we have to depend entirely upon the accuracy of the distance between the lines on the grating—a distance which is measured by a screw advancing through a small proportion of its circumference for each line ruled. If the intervals between the lines are not exactly equal, then there will be an error introduced, notwithstanding every precaution taken, which it is extremely difficult, if not impossible, to correct.

Another error may be introduced in making the comparison of the two extreme lines on the grating with the standard decimeter. This error may, roughly, be said to amount to something like one-half a micron, /. e., one-lialf of one-thousandth of a millimeter. If, then, the entire length of the ruling is fifty millimeters, and the error, say, one ten-thousandth of a millimeter, the wave length may be measured to within one part in 500,000. This is the error