Page:Light waves and their uses.djvu/82

64 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. e., 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, i. e., on 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