Interference (Michelson Interferometer)

[Quasi Particle]

Hello,
.
I have got a Michelson interferometer and measure a laser beam (HeNe @ 633nm). I move the mirror with a step motor of unknown step length and measure the intensity of the beam. I get a nice beat pattern out of that, with "wavelength" of the carrier wave being 14 steps and of the modulation wave being 800 steps of the step motor. Now I want to determine the step length but that suddenly seems to be very complicated.
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The two interfering beams do have the same wavelength, so I would think that this is the wavelength of the carrier wave. But then, there would be no modulation.
Then I remembered that one of the waves "moves", i.e. there is a varying phase difference, and thought that it would be quite interesting to know the phase speed, but here are my formulae:
.
a=k_{c}x - \omega_{c}t is the phase
v=\frac{\omega_{c}}{k_c} is the phase speed
\omega_{c}=\frac{2 \pi c}{\lambda_{c}} is the angular frequency of the carrier wave
k_c=\frac{2 \pi}{\lambda_{c}} is the wave number of the carrier wave
which gives the velocity v=c and I'm quite sure I didn't move the mirror at light speed.
.
Please can you give me a clue where I'm mistaken?
Cheers!

 

[member 553083]

Your mistake is that you have confused the phase speed with the speed of the step motor. The phase speed is the speed at which the phase difference between the two interfering beams is changing, and this has nothing to do with the speed of the step motor.To determine the step length, you need to calculate the period of the modulation wave (the time it takes for one full cycle of the modulation wave). Then divide the total number of steps taken by the step motor during this period by the period to get the step length.