138 Light Waves and Their Uses
one to the disc which is brighter at the center. It will be noted that in the case of the slit the distances between the zero points are all alike. In the case of the disc the curve is still of the same general form, but the distance to the first zero position is no longer equal to the others, but is 1.22 as great. Hence, if the distances between the zero points are equal, as shown in the figure for the full curve, we know the
source is rectangular. But if the distance to the first zero point is 1.22 times as great as the distances between the succeeding zero points, we know that we are observing a uniformly illuminated circular object. The next interval would determine in this case, as in the first, the diameter of the object viewed.
In the case of the slit the distances between the zero points are rigorously equal, and it may be of interest to note that the visibility at the second maximum is something like one-fourth of the visibility at the first. So there is no possibility of deception in noting the point at which the fringes disappear; indeed, the disappearance can be so sharply determined that we may measure the corresponding distance be
Interference Methods in Astronomy 139
tween the slits to within 1 per cent, of its whole value, and so determine the width of the line source w’ith a corresponding degree of accuracy.
The visibility curve shown in Fig. 100 represents the case in which the source is a double disc — a double star, for instance, in which the discs have appreciable magnitude. The envelope of the curve, which is drawn full, corresponds to the circular form of the separate discs, and from this curve we can determine the size of the separate discs, provided they are equal. The dotted curve tells us that we are dealing with a double object. Hence, if in observing a heavenly body we obtain a visibility curve of this form, we infer that we are dealing with a double star.
There is a difficulty in carrying out such observations, especially when w^e are observing a very small object or a very close double star. For in this case the slits have to be separated rather widely, and the angle between the rays from the two slits, when they come together, is rather large. Hence, the distance between the interference fringes is correspondingly small, as was shown in a previous lecture, and this distance becomes less and less as the angle becomes greater and greater. When we approach the limit of resolution of the telescope, the fringes are so small that a rather high power eyepiece must be used in order to see