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

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Light Waves and Their Uses

increase the difference in path between the two interfering beams, then, as was explained above on p. 58, these interference fringes would move across the field of view. Now, in this case, since the light which we are using consists of waves of a single period only, there will be but one set of fringes formed, and consequently the difference of path between the two interfering beams can be increased indefinitely without destroying the ability of the beams to produce interference. It is perhaps needless to say that this ideal case of homogeneous waves is never practically realized in nature.

What will be the effect on the interference phenomena if our source of light sends out two homogeneous trains of waves of slightly different periods ? It is evident that each train will independently produce its own set of interference fringes. These two sets of fringes will coincide with each other when the difference in the lengths of the two optical paths in the interferometer is zero. When, however, this difference in path is increased, the two sets of fringes move across the field of view with different velocities, because they are due to waves of different periods. Hence, one set must sooner or later overtake the other by one-half a fringe, i, r»., the two systems must come to overlap in such a way that a bright band of one coincides with a dark band of the other. When this occurs the interference fringes disappear. It is further evident that the difference of path which must be introduced to bring about this result depends entirely on the difference in the periods of the two trains of waves, ?. r\, 011 the difference in the wave lengths, and that this disappearance of the fringes takes place when the difference of path contains half a wave more of the shorter waves than of the longer. Hence we see that it is possible to determine the difference in the lengths of two waves by observing the distance through which the mirror C must be moved in

Interference Methods in Spectroscopy 65

passing from one position in which the fringes disappear to the next.

If the two homogeneous trains of waves have the same intensity, then the two sets of fringes will be of the same brightness, and when the bright fringe of one falls on the dark fringe of the other, the fringes disappear entirely. If, however, the two trains have different intensities, one set of fringes will be brighter than the other, and the fringes will not entirely disappear when one set has gained half a fringe on the other. In this case the fringes will merely pass through a minimum of distinctness. We see then that, if our source of light is double, i. e., sends out light of two different wave lengths, we should expect to see the clearness or visibility of the fringes vary as the difference of path between the two interfering beams was increased.

If we invert this process and observe the interference fringes as the difference in path is increased, and find this variation in the clearness or visibility of the fringes, it is proved with absolute certainty that we are dealing with a double line. This is found to be the case with sodium light, and, therefore, by measuring the distance between the positions of the mirror at which the fringes disappear, we find that we actually can determine accurately the difference between the wave lengths of the two sodium lines. In order to carry the analysis a step farther, suppose that we magnify one of these two sodium lines. It would probably appear somewhat like a broad, hazy band. For the sake of simplicity, however, we will suppose that it looks like a broad ribbon of light with sharp edges. The distance between these edges, i. e., the width of this one line, if the sodium vapor in the flame is not too dense, is something like one-fiftieth, or, perhaps, in some cases as small as one-hundredth, of the unit we have adopted — the distance between the sodium lines.