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This may seem like a simple question, but I cant seem to make any headway.

Consider the following; I have two beams of light, a reference beam $(A=\cos(wt))$ and phase shifted beam $(B=\cos(wt+\phi))$.

What is the normal way (say in a lab) that $\phi$ is detected & measured with respect to the reference beam?

I believe an interferometer is used, but I dont understand how this yields a measurement.

Thanks for any insight.

EDIT: I don't know if I've explained this very well. I think better in pictures, so here is a VERY crude diagram of my thought experiment.

enter image description here

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2 Answers

up vote 2 down vote accepted

First remove the "process" step from your diagram so that you are comparing two beams of light with $\cos(\omega t)$. Let's say, for the sake of simplicity, that they can be considered plane waves, and your interferometer combines them at a small angle, so that you see a series of stripes (bright and dark fringes) on your screen.

Now add the "process" step, being careful not to disturb any other part of the interferometer. This causes a phase difference $\phi$ between the beams. The positions of the bright and dark fringes will shift. Say $d$ is the distance between two crests or troughs (brightest parts of two bright fringes or darkest parts of two dark fringes), and $\Delta x$ is the distance by which the fringes shifted when you introduced the phase difference.

Then, $$ \phi\bmod{2\pi} = 2\pi\Delta x / d$$

Note that you won't be able to tell if $\phi > 2\pi$.

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That is very helpful, thanks. –  Michael Oct 11 '12 at 16:53
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Briefly, one technique for observing phase shifts in light is Phase Contrast microscopy which garnered Fritz Zernike the 1953 Nobel prize in physics.

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Not quite what I had in mind, but thanks for the input. It's an interesting process I'll have to read up on. –  Michael Oct 11 '12 at 16:53
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