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
Light Waves and Their Uses
8 by a plane surface. The interferometer is now changed into the form illustrated in Fig. 33. It will now be noted that the source need no longer be a point or a slit, but may be a broad flame; and the object whose position is to
be measured is no longer a fine line or a slit, but a flat surface. The width of the fringes may be made as great as we please without any sacrifice in the brightness of the light. The corresponding increase in accuracy is from twenty to one hundred fold. We may conveniently restrict the term interferometer to this arrangement, in which the division and the union of the pencils of light are effected by a transparent plane parallel plate. It is important to note that the path of the two pen
cils after their separation by the first plate is entirely immaterial ; for example, either or both pencils may suffer any number of reflections or refractions before they are reunited by the second plate, without affecting in any essential point the efficiency of the interferometer, provided that the differ