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

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Light Waves and Their Uses

either skle. The corresponding intensity curve is shown in Fig. 96.1

If we had two such apertures instead of one, the appearance would be all the more definite; but the two apertures together produce, in addition, interference fringes very much finer than the others, but very sharp and clear. The intensity curve corresponding to these two slits is shown in Fig. 97. In this case it is easy to distinguish the successive maxima, and the atmospheric disturbances are very much less harmful than in the case of the more indefinite phenomenon.

Fig. 98 represents the appearance of the diffraction pattern due to two slits when a slit, instead of a point, is used as the source of light. The appearance of the two patterns is not essentially different, that due to the slit being very much brighter. In the case of a point source there is so little light that it is more difficult to see the fringes. Here the same large fringes are visible as before, but over the central bright space there is a number of very fine fringes. The two central ones are particularly sharp, so that it is easy to locate their position if necessary, but still easier to determine their visibility. This clearness is the essential point we have to consider, because the size of the object determines the clearness of the fringes. We find that if we gradually increase the width of the source, the fringes grow less and less distinct, and finally disappear entirely. If we note the instant when the fringes disappear, we can calculate from the dimensions of the apparatus the width of the

FIG. 96.

1 This ignores the diffraction bands parallel to tho shorter sides of the rectangle, which are usually inconspicuous.

Interference Methods in Astronomy 135

source. Or, if we alter the dimensions of the apparatus and observe when the fringes cease to be visible in our observing telescope, we have the means of measuring the diameter of the source, which may be a double star, or the disc of one of Jupiter's satellites, or one of the minor planets.

We may get some notion of the relation which exists between the clearness of the fringes and the size of the object when the fringes disappear, by considering a simple case like that of a double star.

Suppose we have two slits in front of the object glass of a telescope focused on a single star. At the focus the rays from the two slits come together in condition to produce interference fringes, and the fringes always appear when the source is a point. Suppose we have in the field of view another star. It will produce its own series of fringes in the focus of the telescope. We shall then have two similar sets of fringes in the field of view. If, now, the two stars are so near together that the central bright fringes of the tw’o systems coincide, then the two sets of fringes will reinforce each other. If, however, one of the stars is just so far away from the other that the angle between them is equal to the angle between the central bright band and its first adjacent minimum, then the maximum of one system of fringes will fall upon the minimum of the other set, and the two will efface each other so that the fringes disappear. Hence the fringes disappear when the angle subtended by the source is equal to the angle subtended by half the breadth of the fringes, viewed from the objec