Roberto Martins Searching for the Ether
DIO 17
Fig. 3. Following a theoretical analysis by Adolf von Hamack, Courvoisier accepted that the angle of reflection of light in a moving mirror is influenced by its motion through the ether, and that there is a second-order effect that can be measured in the reference frame of the mirror.
Taking into account this “principle of the moving mirror”, Courvoisier predicted that the angle between the local vertical (zenith) and the direction of observation of a given star would be slightly different from the angle between the zenith and the direction of the star observed using a mercury mirror (Fig. 4).
Fig. 4. Courvoiser compared the direct measurement of the direction of a star with its direction observed by reflection on a mercury mirror.
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Roberto Martins
Searching for the Ether
DIO 17
In this specific case, the contraction of the Earth could produce no effect, because both measurements were made relative to the same reference (the local vertical) and the surface of the mercury mirror is, of course, perpendicular to the local vertical, whatever the changes that the gravitational field could undergo due to Lorentz contraction. The predicted effect was a small systematic difference between the direct and the reflected angles, which should depend on the direction of the observatory relative to the motion of the Earth through the ether.
Fig. 5. Elamack’s diagram for analyzing the reflection of light in a moving mirror. The initial position of the mirror is S, and after a time 81 its position is S'. AA' is a wave front of the incident light beam, and BE is a wave front of the reflected beam.
Let 9 be the angle of incidence and 9' the angle of reflection of a light ray in a moving mirror, measured relative to the ether (Fig. 5).10 According to Eiamack's analysis, instead of 9=9' the following equations would hold:
sin 9' = (1 - P2) sin 9 / (1 + 2P cos 9 + P2) (4)
cos 9' = [(1 + P2) cos 9 + 2P] / (1 + 2P cos 9 + P2)(5)
16 In his equations Courvoisier used 9 as a symbol of sidereal time, but in this particular derivation we are following Hamack's notation in his paper “Zur Theorie des bewegten Spiegels” (ref. 15).
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