Light Waves and Their Uses
the actual experiment, however, they are all superposed. At the middle point, where the two paths are equal, all the
colors will be superposed, the re-
Jsult being a white central band. 1 At no other point will this be true, I III II an j resuit wiu be a series of
colored fringes symmetrically disposed about the central white fringe, the succession of colors being exactly the same as in the case of thin films (c/. Plate II).
The breadth of the fringes is determined by the smallness of the angle under which the two pencils meet. This is shown in Fig. 30. FIG gg In the right-hand figure the angle
between the pencils is smaller than in the other, while the breadth of the fringes is correspond-ingly greater in the former than in the latter. The exact
relation is readily obtained. We have only to note that ac is the wave length I (very nearly) and be is (very nearly) the width b of a fringe; whence, if e is the very minute angle
Microscope, Telescope, Interferometer 35
at b (which is the same as the angle between the directions
of the interfering pencils), b = ~; or, in other words, the
width of the fringes is proportional to the wave length of the light, and inversely proportional to the angle between the pencils.
Thus, if the pencils converge from two apertures a quarter of an inch apart, and meet at a screen ten feet away, the breadth of the fringes will be one-hundredth of an inch. The importance of using a very small angle will be noted.
In this simple form of interferometer the angle can be made small only by bringing the two apertures very near together, which seriously diminishes the efficiency of the instrument; or by increasing the distance from the openings to the fringes, or by using a high magnification, which enfeebles the light, already very faint in consequence of having to start from a pinhole or a narrow slit s (Fig- 31) and to pass through the narrow apertures a and b. There is, therefore, but little advantage in this form of interferometer over the corresponding older analogues (microscope and telescope).
An important improvement may be effected by bending one or both the rays ap, bp by reflections in such a way as to diminish the angle at p, as shown in Fig. 32.
A further improvement is effected by replacing the apertures a and b by mirrors; and, finally, by replacing the slit