CONFERENCE ON MICHELSON-MORLEY EXPERIMENT 369
intensity, one passing to the mirror Mx and the other to M2. From there they are reflected back to M3, where they recombine and pass to the eye through a telescope focused on Mx and M2• Two purposes are accomplished by the use of plane-polarized light : first, the noninterfering rays indicated by the dotted lines, which would be produced with natural light, are completely eliminated; and, second, the recombining beams can be adjusted to perfect equality of intensity by varying the relative reflecting powers of Mz and M2. Be
cause there are two more glass-air interfaces to be traversed by the upper beam than by the lower, it is impossible to equalize both components of natural light in this way.
The high sensibility necessary because of the short paths is secured chiefly by the simple device of raising one-half of the surface of mirror M2 a small fraction of a wave-length above the other, the dividing line between the two levels being straight and as sharp as possible. The mirror used was made by covering part of a plane plate with a flat sharp-edged microscope cover-glass and applying the extra thickness by cathode deposition of platinum, thereafter giving the whole plate a fully reflecting coat. I ran across the suggestion of using such a divided mirror in interferometry some years ago, but am unaware to whom the credit for it belongs.
is split by a thin platinum film into two parts of nearly equal
Fig. 9
Fig. 10
37°
ROY J. KENNEDY
The theory of the arrangement is as follows: The interference phenomena will be the same as if the mirror M2 were replaced by its image in Mz. Under the conditions of the experiment, where the paths are nearly equal, Mx is perpendicular to the beam incident on it, and the reflected beams are brought nearly to parallelism, the image of M2 will be nearly parallel and coincident with the face of Mx. Elementary theory shows that the resulting interference pattern then practically coincides with Mx. It would needlessly complicate this discussion to develop the general theory of interference for all inclinations of the mirrors; the experimentally realized case of near parallelism alone is necessary.
Let Figure 10 represent a greatly exaggerated cross-section of Mx and the image of M2, normal to their planes and to the dividing line in M2. Mx lies in the plane x = o, and the levels of M2 are at equal distances on opposite sides of a parallel plane at the distance x from Mx. Let a monochromatic wave, in which the displacement is given by
fall on Mx and M2 from the left. At the surface of Mx the displacement in the reflected wave is then given by
if we ignore the loss through imperfect reflection. The displacement in the plane of Mx in the wave reflected from the upper part of M2 is
£x — a cos co(/+e)
The square of the resultant displacement is then
= O'2 j cos GO(t“j-é) “f"cos co |~f-€---—-—-
This can be reduced to the form