Interference Methods in Astronomy 183
the interference fringes, we should have a means of making an independent measurement of the size of objects which are practically beyond the power of resolution of the most powerful telescope. The principal object of this lecture is to show the feasibility of such methods of measurement. For this purpose, however, the circular fringes that we have been investigating are not very well adapted; they are not very sharply defined; there is not enough contrast between them.
However, there is a relation which can be traced oat between the clearness of the diffraction fringes and the size and shape of the object viewed.
This relation is very complex.
The result of such calculation is that the intensity is greatest at the center, whence it rapidly falls off to zero at the first dark band. It then increases to a second maximum, where it is not more than one-ninth as great as in the center. What we should have to observe, then, is the contrast between these two parts—one but one-ninth as marked as the other and confused more or less by atmospheric disturbances. In case of a rectangular aperture the intensity curve is somewhat different, in that the maxima on either side of the central band are considerably greater, so that it is somewhat easier to see the fringes. ’ In case of the rectangular aperture the fringes are parallel to the long sides of the rectangle. The appearance of the diffraction phenomenon in this case is illustrated in Fig. 95. The pattern consists of a broad central space, whose sides are parallel to the sides of the rectangular slit, and of a succession of fringes diminishing in intensity 011
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
1 This ignores the diffraction bands parallel to tho shorter sides of the rectangle, which are usually inconspicuous.