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
136 Light Waves and Theib Uses
tive. This angle is easily calculated. Thus if I represent the wave length and s is the distance between the two slits, then
the angle is equal to ^• Hence, if we know the length
of the light wave (we can take it as one fifty-thousandth of an inch if we choose), by measuring the distance between our slits when the fringes disapj)ear we have the means of measuring the angular distance between double stars. y/ In the case of a single-slit source we can also get some sort of an idea of the conditions which prevail when the fringes disap{>ear. For we may conceive the slit source to be divided into a number of line sources, parallel and adjacent to each other. Then each line source would form its own set of fringes, and when the angle between the two outside lines, i. ethe edges of the slit, is equal to the angle subtended by the distance of the first dark band from the center, the fringes again overlap in such a way as to disappear. The value of this angle is easily found to be So,
supposing that we had such an object in the heavens as a narrow band of light, we have the means of finding its width. If, instead of a slit, we used a circular opening as a source, there is a little more difficulty in the mathematical analysis. In this
case the coefficient of - , instead of being 1 as in the second
case, or i as in the first case, is found to be 1.22. In observing such an object we measure the distance between our two slits when the interference fringes have just vanished, and compute the angular magnitude of the object by using this coefficient. If we knew the distance to the object, we could calculate also its actual diameter.
The curve representing the clearness of the fringes as the slits approach is rather interesting. It varies with the form