CONFERENCE ON MICHELSON-MORLEY EXPERIMENT 375
confirms, by an independent calculation, some of Righi’s results, which is a matter of great importance, since the accuracy of his work has been called in question.1
2. REFLECTION FROM A MOVING MIRROR
We begin by obtaining certain general formulae for the reflection of light from a moving mirror. Two cases are considered: (a) the direction of motion of the mirror coincides with the direction of the rays of light before reflection; (b) the direction of motion of the mirror makes an angle 0 with the direction of the rays of light.
a) Denote the velocity of light by c and the velocity of the
mirror by v. Let h represent the tangent of the angle of inclination of the mirror to the direction of motion.
In Figure 11, AZ represents the front of a wave advancing on the mirror at A. While the mirror moves from AL to A'L', the portion of the wave at Z traverses the distance ZLr. Therefore, denoting the angle A'AL' by a, we have
tan a = J^= (1 —|)Ä= (1 —/3)Ä ,
which gives the position of the equivalent fixed mirror.
Similarly, ArL is the position of the equivalent fixed mirror for a ray coming from the opposite direction CA; and if we denote CA'L by y, we have
tan 7 = (1 + ß)h .
1 See Observatory, 44, 340-341, 1921.
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E. R. HEDRICK
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--=— ,
h
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) ,
while
tan 7=i+jS(cos 0 —sin 0) .
3. APPLICATION TO THE MICHELSON-MORLEY EXPERIMENT
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