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.
.
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:
.
[tex]a=k_{c}x - \omega_{c}t[/tex] is the phase
[tex]v=\frac{\omega_{c}}{k_c}[/tex] is the phase speed
[tex]\omega_{c}=\frac{2 \pi c}{\lambda_{c}}[/tex] is the angular frequency of the carrier wave
[tex] k_c=\frac{2 \pi}{\lambda_{c}}[/tex] 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!

 

[Nate810]

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.

 

[quicknote]

Hello,

As a fellow scientist, I can understand your confusion. Let me try to provide some clarification on the concept of interference and how it applies to the Michelson interferometer in your experiment.

Interference occurs when two or more waves interact with each other, resulting in a pattern of constructive and destructive interference. In the case of the Michelson interferometer, the two beams of light (from the beam splitter and the moving mirror) are interfering with each other, resulting in the beat pattern you observed.

Now, in terms of the wavelength of the carrier wave and the modulation wave, it is important to note that the carrier wave is the original beam of light, while the modulation wave is the same beam of light, but with a varying phase difference due to the movement of the mirror. So, the wavelength of the carrier wave remains the same, but the modulation wave has a slightly different wavelength due to the phase difference.

In your formula, the phase speed is calculated as the ratio of the angular frequency (omega) to the wave number (k). However, in this case, the wave number (k) for the modulation wave is not the same as the wave number for the carrier wave. This is because the modulation wave has a different wavelength due to the phase difference.

So, in conclusion, you are not mistaken, but you may need to consider the different wavelengths of the carrier wave and the modulation wave when calculating the phase speed. I hope this helps. Keep up the good work in your experiments!