On Sep 10, 2009, at 8:27 PM, Harry Veeder wrote:
----- Original Message ----- From: Horace Heffner <hheff...@mtaonline.net> Date: Thursday, September 10, 2009 8:02 pm Subject: Re: [Vo]:Michelson-Morley Interferometer experiment finally done correctly?On Sep 10, 2009, at 2:17 PM, Harry Veeder wrote:I still find the sagging beam splitter explanation inconsistent with what is observed. As the beam splitter rotates into and out of the vertical orientation this is when the supposed sagging is nil so thepattern's> movement should change direction during this interval. When the beamsplitter is oriented horizontally this is when sagging is at amaximum> so the pattern should bemoving the fastest. Where have I gone wrong? harryThe pattern moves when there is a change in the two path lengths. That movement is maximum when the path length difference *changes* most rapidly, not when one path is at a maximum or minimum length with respect to each other.Ok, but the switch in direction of movement of the pattern must also be explained by the deflection of the beam splitter. This switch must be a function of the direction of deflection of the beam splitter w.r.t. thelaser. Since this direction of deflection only changes twice w.r.t. tothe laser, the switch in direction of the pattern only occurs twice. Isthis correct? harry
I don't know why you refer to the direction of the beam splitter w.r.t the laser. Direction is not what changes significantly. The beam splitter splits the beam 50/50, always pretty much in the same directions with respect to the base and laser. It is the change in path length that affects the interference pattern. The laser path lengths are probably affected by motions of both the beam splitter and the mirrors, but my main assumption was that it was the beam splitter that was contributing the most. Considering the beam splitter only, it reaches maximum sag twice in each rotation, when the device and laser is on about a 45 degree angle, and the beam splitter is parallel to the horizon plane. At maximum sag, the motion of the interference lines is stopped, and then reverses. The mirror then begins its motion over to the other maximum sag position, which is 180 degrees away. When the beam splitter sags by a few wavelengths the light *direction* is affected almost not at all. However, the path length to the mirror in line with the laser is significantly affected.
The laser hits the splitter at a small spot roughly in its middle. Call the distance from the laser to the splitter spot D. Call the distance from the Splitter spot to the mirror in line with the laser D1. Call the distance from the splitter spot to the mirror to one side of the main beam D2. The path to final exit of the beam slitter toward the lense is D + 2 D1 for the straight path, and D + 2 D2 for the side path. See attached drawing.
When the beam splitter sags towards the laser it moves the spot on the mirror slightly to one side on the mirror, because the mirror sags in a direction 45 degrees to the laser beam. This leaves the path length D2 to the mirror to the side of the beam unchanged, even though the spot on that mirror is laterally displaced, toward the laser. This lateral displacement is not detectable because that displacement is only a small number of wavelengths of light, a few microns since the wavelength is 532 nm. However, the movement of the mirror toward the laser reduces the path length D from the laser to the beam splitter by delta D, while increasing the path length from the laser to the in-line mirror, D1 by delta D. Since the light travels distance D1 twice, the path to the in-line mirror is changed from D + D1 to D - (delta D) + D1 + 2 (delta D) = D + D1 + delta D. The path to the side mirror is changed from D + D2 to D + D2 - delta D. The total difference in path lengths is 2 (delta D). When the mirror swings the opposite direction, the path length difference changes to -2 (delta D). Note that the interference pattern motion has only to do with the change in the difference between the two paths. For half the rotation cycle delta D, and thus the difference, is moving in one direction, the other half it moves the other direction. This matches what is on the video.
Horace Heffner http://www.mtaonline.net/~hheffner/
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