## Path difference and phase difference.

Pardon the pun, but what's the difference between path difference and phase difference (when talking about interfering light waves)?

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 Path difference is the distance one wave (from a coherent source) has to travel from its source to the observer. ie one observers ear may recieve the crest and the other ear recieve the trough. this would give a path difference of 1/2 wavelength. Phase difference is best understood by considering a cosine wave and a sine wave. they are 90degrees out of 'synch' with each other and would produce destructive interference. i hope someone with more brains than me can clarify your quandary. I think i am corect but i am sure someone here can be more specific.

 Quote by bootsam Path difference is the distance one wave (from a coherent source) has to travel from its source to the observer. ie one observers ear may recieve the crest and the other ear recieve the trough. this would give a path difference of 1/2 wavelength. Phase difference is best understood by considering a cosine wave and a sine wave. they are 90degrees out of 'synch' with each other and would produce destructive interference. i hope someone with more brains than me can clarify your quandary. I think i am corect but i am sure someone here can be more specific.
I believe the equation would be phase difference = 2pi/lambda*path difference

Recognitions:
As a beam traverses space, the phase of a ray goes as $$\phi (z) = k n z$$, where k is the wavevector, n the refractive index, and z the distance. The quantity nz (or nd, where d is the thickness of an object) is referred to as the optical thickness. It's easy to make the sitation more complicated- make the refractive index vary with location, for example. Or make it vary with wavelength. Then the phase delay *relative to another ray*, which is the important thing, is given by more complex versions of the above formula.