Conference on the Michelson-Morley experiment held at the Mount Wilson observatory Pasadena, California February 4 and 5, 1927

В начало   Другие форматы (PDF, DjVu)   <<<     Страница 376   >>>




b) If the direction of motion of the mirror makes an angle with the direction of the rays, then from Figure 12 it is clear that the mirror really advances with a velocity

_ v sin 0

V cos 0--=— ,


so that the formulae for this case may be obtained from those of the previous case by putting

/ _ sin 0\

0(cos e-Tj

in place of ß.

If the mirror is inclined at an angle of 450 to the direction of the rays of light, h = 1 and

tan a=i — ß(cos 0 —sin 0) ,


tan 7=i+jS(cos 0 —sin 0) .


In the Michelson-Morley experiment a ray of light from a source S (Fig. 13) meets a half-silvered glass plate, inclined at 450 to its path, at A. A portion is reflected to a mirror at B, parallel to 5^4, from which it is again reflected to pass through the plate at Af and finally into a telescope at T. Another portion is transmitted through the glass plate at A to a mirror at C, perpendicular to 5^4, from which it is returned to the glass plate at Ar and from there a further portion is reflected into the telescope at T. When the mirrors are set as described, with absolute accuracy, we call the experiment the “ideal Michelson-Morley experiment.” We wish to compute the angle T'A'T. '

We assume that the earth and the apparatus are moving through the ether in a direction making an angle 0 with the path of the rays SA.

It will be necessary to determine the position of the equivalent fixed mirror at B.

For convenience denote ß(cos 0 —sin 0) by £. Then the angle CAB = 2a where tan a = 1 — £.

In Figure 14, if BE is the wave front of the ray reflected from A and if the mirror at B advances from BM to BrMf (a distance r in


Fig. 14

the direction 9) while the portion of the wave front at E advances to M\ then BMr is the position of the equivalent fixed mirror. Denote the angle MBM! by p; then


where GM' is perpendicular to BM.

GM' — MM' sin 2a = r sin 0; BG—BM-\-MM' cos 2a;

EM r

cos 2a ; P EM+MM' *