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

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Light Waves and Their Uses

distance apart is the same as that of the lines of curve 2. The j>eriod of the visibility curve is the same as that of 2, but instead of going to zero it merely goes to a minimum at /. Inversely, when we get such a curve as this we know that one of the lines is brighter than the other—just how much brighter can be learned from the ratio of the maximum and minimum ordinates.

Curve 5 is that due to a single broad source of uniform intensity throughout. It will be noted how quickly the fringes lose their distinctness. Curve 6 is that due to a broad source which is brighter in the middle than at the edges. The distribution in this case is supposed to follow the exponential law. The corresponding visibility curve does not exhibit maxima and minima, but gradually dies out and remains at zero. Curve 7 corresponds to a double source each of whose components is brighter in the middle. Curve 8 represents a triple source each of whose components is a simple harmonic train of waves of the same intensity. Curve 9 represents the visibility due to a triple source in which the outer components are much fainter than the middle one.

We might go on indefinitely constructing on the machine the visibility curves which correspond to any assumed distribution of the light in the source. The curves presented will suffice to make clear the fact that there is a close connection between the distribution of light in any source and the visibility curve which can be obtained with the use of that source. It is, however, the inverse problem,

i. e., that of determining the nature of the source from observation of the visibility curve, in which the greatest interest lies.

In order to determine by this method the character of the source with which we are dealing, we must find our visibility curve by turning the micrometer screw of the inter

Interference Methods in Spectroscopy


ferometer and noting the clearness of the fringes as the difference of the path varies. We then construct a curve which shall represent this variation of visibility on a more or less arbitrary scale, and compare it with one of the known forms, such as those shown in Fig. 58. There is, however, a more direct process. The explanation of this process involves so much mathematics that I shall not undertake it here. It will be sufficient to state that the harmonic analyzer cannot only be used as has been described, but is also capable of analyzing such visibility curves. Thus, if we introduce into the instrument the curve corresponding to the visibility curve, by making the distances of the connecting rods from the axis proportional to the ordinates of the visibility curve, and then turn the machine, it produces directly a very close approximation to the character of the source. For example, take curve 2 of Fig. 58. By its derivation we know that it corresponds to a double source each of whose components is absolutely homogeneous. If we introduce this curve, or rather the envelope of it, into the machine, it will give a resultant which represents the character of the source to a close degree of approximation. The actual result is shown in Fig. 59, in which the ordinates represent the intensity of the light. We thus see that the machine can operate in both ways, L <?., that it can add up a series of simple harmonic curves and give the resultant, which in the case before us is the visibility curve, and that it can take the resultant curve and analyze it into its components, which here represent the distribution of the light in the source.

Now the question naturally arises as to how the observations by which the visibility curve is determined are conducted; also as to what units to adopt, and what scale