13.8 DIVISION OF AMPLITUDE. MICHELSON+ INTERFEROMETER Interference apparatus may be conveniently divided into two main classes, those based on division of wave front and those based on division of amplitude. The previous examples all belong to the former class, in which the wave front is divided laterally into segments by mirrors or diaphragms. It is also possible to divide a wave by partial reflection, the two resulting wave fronts maintaining the original width but having reduced amplitudes. The Michelson interferometer is an important example of this second class. Here the two beams obtained by amplitude division are sent in quite different directions against plane mirrors, whence they are brought together again to form interference fringes. The arrangement is shown schematically in Fig. 13N. The main optical parts consist of two highly polished plane mirrors M, and M2 and two plane-parallel plates of glass G, and G2. Sometimes the rear side of the plate G, is lightly silvered (shown by the heavy line in the figure) so that the light coming from the source S is divided into (1) a reflected and (2) a transmitted beam of equal intensity. The light reflected normally from mirror M, passes through G, a third time and reaches the eye as shown. The light reflected from the mirror M2 passes back through G, for the second time, is reflected from the surface of G, and into theFIGURE I3N Diagram of the Michelson interfer- omelet. eye. The purpose of the plate GE, called the compensating plate, is to render the path in glass of the two rays equal. This is not essential for producing fringes in mono- chromatic light, but it is indispensable when white light is used (Sec. 13.11). The mirror M1 is mounted on a carriage C and can be moved along the well-machined ways or tracks T. This slow and accurater controlled motion is accomplished by means of the screw V, which is calibrated to show the exact distance the mirror has been moved. To obtain fringes, the mirrors M1 and M; are made exactly perpendicular to each other by means of screws shown on mirror M3. Even when the above adjustments have been made, fringes will not be seen unless two important requirements are fullled. First, the light must originate from an extended source. A point source or a slit source. as used in the methods previously described, will not produce the desired system of fringes in this case. The reason for this will appear when we consider the origin of the fringes. Second. the light must in general be monochromatic, or nearly so. Especially is this true if the distances of M, and M; from G, are appreciably different. An extended source suitable for use with a Michelson interferometer may be obtained in any one of several ways. A sodium flame or a mercury are, if large enough, may be used without the screen L shown in Fig. ISN. If the Source is small, a ground-glass screen or a lens at L will extend the eld of view. Looking at the mirror M1 through the plate 6,, one then sees the whole mirror lled with light. In order to obtain the fringes, the next step is to measure the distances of M, and M3 to the back surface of G, roughly with a millimeter scale and to move Ml until they are the same to within a few millimeters. The mirror M2 is now adjusted to he perpendicular to M, by observing the images of a common pin, or any sharp point, placed between the source and 6,. Two pairs of images will be seen, one coming from reection at the front surface of G, and the other from reection at its back surface. When the tilting screws on M; are turned until one pair of images falls exactly on the other, the interference fringes should appear. When they rst appear, the fringes will not be clear unless the eye is focused on or near the back mirror M1, so the observer should look constantly at this mirror while searching for the fringes. FIGURE 13-0 Formation of circular fringes in the Michelson interferometer. When they have been found, the adjusting screws should be turned in such a way as to continually increase the width of the fringes. and nally a set of concentric circular fringes will be obtained. M1 is then exactly perpendicular to M1 if the latter is at an angle of 45 with GI