Michelson interferometer and Doppler effect

[Kromboy85]

Homework Statement

Hello, I'm working on an experiment that involves a Michelson interferometer and doppler effect.
Here is the description of the apparatus.

Michelson interferometer is set up with one moving arm and microwave is transmitted and received.

With the beam splitter splitting 50/50 I then move the moving arm on a frictionless surface at a constant velocity. I am tracking the velocity of the moving arm and this will be the control value to which I'll compare my experimental value.

On the oscilloscope, I can see the peaks in the microwave intensity and can then find the fringe distance which I believe would simply equal wavelength? Or is it 2 wavelengths?

Homework Equations

E(measured) = Cos(2*Pi*f*m*v/2). M is an integer, negative or positive. I dropped the variable thinking it'll be a 1 or -1

I simplify the equation down to E(measured) = Cos(Pi*f*v)
Which I again simplify to get the velocity V = (1/Pi*f)*arccos(E)

The Attempt at a Solution

Here are the values I have so far.

I have the voltage reading from the receiver which I can deduce the distance and time between peaks from. But the voltage themselves do not hold any meaning since the receiver was amplified.

For the velocity equation so that I can independently calculate velocity and compare to the value earlier:

V = (1/Pi*f)*arccos(E)
I have the Pi, and the frequency. But I cannot find E for my life.
I've been trying for 3 hours and I just don't get it.

Am I lacking data to be able to figure out E? Or is it even necessary? I'm using a microwave source, I don't even know why electric field would be used in Michelson interferometer.

If anyone has any idea how I would obtain E with the above data that I have, please let me know.**** Update!

So there is this phrase "where v is the speed of the cart, so you can see fringes on the oscilloscope. The measured
(average) field is a maximum every time Δ= 2mπ , where m is an integer (positive or negative).
How can you measure velocity by counting fringes?"

I think that is supposed to be a hint. But I'm having trouble making sense of that. How exactly would I use the number of fringes I have to measure velocity?

Thanks for the help

 

[mark726]

!
Thank you for sharing your experiment and questions with us. It sounds like you are conducting an interesting study on the Michelson interferometer and the Doppler effect. Let me try to address your questions and provide some guidance.

Firstly, regarding the fringe distance, it is indeed equal to one wavelength. This is because the Michelson interferometer relies on the interference of two light waves, one reflected from the moving arm and one reflected from the stationary arm. As the moving arm travels a distance equal to one wavelength, it will cause a phase difference of one wavelength between the two waves, resulting in a fringe on the oscilloscope.

Regarding your attempt at a solution, it seems like you are on the right track. The equation you have derived is correct for calculating the velocity. However, to obtain the electric field (E) value, you will need to use the equation you mentioned: E(measured) = Cos(2*Pi*f*m*v/2). This equation takes into account the interference of the two light waves and the velocity of the moving arm. So, by measuring the distance and time between peaks on the oscilloscope, you can calculate the velocity and then use it in this equation to obtain the E value.

As for the phrase "where v is the speed of the cart, so you can see fringes on the oscilloscope. The measured (average) field is a maximum every time Δ= 2mπ , where m is an integer (positive or negative). How can you measure velocity by counting fringes?", it is indeed a hint. By counting the number of fringes that pass through the oscilloscope, you can calculate the distance traveled by the moving arm (since each fringe corresponds to one wavelength). And by dividing this distance by the time between peaks, you can calculate the velocity.

I hope this helps clarify some points and gives you a better understanding of the experiment. Best of luck with your research!