Fabry-Perot and Michelson Interferometry: A Fundamental Approach - Comments

[Charles Link]

Charles Link submitted a new PF Insights post

Fabry-Perot and Michelson Interferometry: A Fundamental Approach

Continue reading the Original PF Insights Post.

 

[houlahound]

Only skimmed ATM, looks like another great insight.

Thanks.

 

[Greg Bernhardt]

Great first Insight Charles!

 

[Charles Link]

Perhaps one thing worth mentioning in more detail that I only included in one sentence in the article is that it can also be applied to sinusoidal r-f voltage signals traveling on a transmission line and incident on an interface where the characteristic impedance changes. The same reflection and transmission coefficients apply with $n_1$ replaced by $\frac{1}{Z_1}$, and $n_2$ replaced by $\frac{1}{Z_2}$, and the electric field $E$ replaced by voltages. (In the r-f case I don't think they call them "Fresnel" coefficients, but the equations are the same with the replacement just mentioned. And of course the energy/power goes as $V^2/Z$ ) .It will even work for two voltage pulses traveling on a transmission line. Instead of having the signals $\pi$ out of phase, one of them can be a pulse with a negative voltage. @Dale I think you are an electrical engineer=perhaps you would find the r-f case of interest.

 

[houlahound]

That would be good to edit into the original article, not everyone will see your last post.

 

[Charles Link]

That would be good to edit into the original article, not everyone will see your last post.

Thank you @houlahound I took your suggestion and added a paragraph at the bottom. :)

 

[Charles Link]

Just one additional comment that doesn't need to be part of the article: I believe the radar that the police use is essentially a Michelson type configuration, possibly with microwaves, where the vehicle being measured for its speed is basically one of the Michelson mirrors. The returning Doppler shifted sinusoidal signal is heterodyned with the internal reference signal (the two signals are combined and the beat frequency observed). For microwaves, an optical type beamsplitter would not be necessary, but otherwise, the principles are similar.

 

[houlahound]

I think microwave speed detectors for police use are obsolete. They have laser systems now. From what I can tell.

What you said prolly still holds tho.

 

[Charles Link]

I think microwave speed detectors for police use are obsolete. They have laser systems now. From what I can tell.

What you said prolly still holds tho.

I should point out that for the case of the moving Michelson mirror, there are two ways of analyzing the system that yield identical results: 1) As the interference of the two signals that causes constructive or destructive interference with the result changing with time because of the changing relative phase of the two signals due to the changing path distance as a function of time 2) As a frequency shift (Doppler shift) of the returning signal from one of the mirrors.

 

[vanhees71]

That's a very nice Insights article!

 

[Charles Link]

That's a very nice Insights article!

Thank you @vanhees71

 

[Greg Bernhardt]

btw, Charles just published his second Insight here:
https://www.physicsforums.com/insights/permanent-magnets-ferromagnetism-magnetic-surface-currents/

 

[Charles Link]

A student just posted a homework question involving the Michelson interferometer in the form where the source is a diffuse source rather than a plane wave. The concepts presented in this Insight article are still relevant, and anyone with an interest in interferometry may find this homework question of interest: https://www.physicsforums.com/threa...michelson-interferometer.933638/#post-5902650 $\\$ This experiment of the interference fringes of the sodium doublet using a Michelson interferometer is performed on occasion in an Optics class that includes laboratory experiments. My classmates and I performed such an experiment in the upper level undergraduate Optics course at the University of Illinois at Urbana in 1976. We did successfully show that the lines of the doublet are separated by $\Delta \lambda \approx 6.0$ Angstroms.

 

[Charles Link]

An additional item came up in another post today, https://www.physicsforums.com/threads/interference-puzzle.942715/#post-5963655 , where a beamsplitter can be half-silvered, and the result is a $+\pi/2$ phase change that occurs on both reflections. The reason for a phase change of $\pi/2$ that occurs between transmitted and reflected beams is perhaps of quantum mechanical origins, but there may also be a completely classical explanation for this result (see the discussion in the thread along with the "links" supplied in the discussion). $\\$ In any case, upon introducing this $+\pi/2$ phase shift on both reflected beams, interference along with conservation of energy is found to occur, just as in the case treated in this Insights article of the dielectric beamsplitter that has phase shifts of $\pi$ and zero for the reflections, external and internal, off of the uncoated (no anti-reflection coating) face of the dielectric beamsplitter. Upon introducing the $+ \pi/2$ phase shifts for the half-silvered beamsplitter, the rest of the calculation for the resulting energy distribution proceeds just as in the purely classical case.

 

[Charles Link]

Here is another posting of a homework question that came up involving the Michelson interferometer, and the sodium doublet at 589.0 and 589.6 nm. It is a little simpler than the homework question of post 13. https://www.physicsforums.com/threads/interferometer-2-spectral-lines.944019/#post-5973375