Path difference and phase difference.

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Discussion Overview

The discussion centers on the differences between path difference and phase difference in the context of interfering light waves. Participants explore the definitions and implications of these concepts, including their mathematical relationships and the effects of varying conditions such as refractive index.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants define path difference as the distance a wave travels from its source to an observer, noting that it can result in different waveforms reaching the observer (e.g., crest vs. trough).
  • Phase difference is described in terms of wave synchronization, with examples such as cosine and sine waves being 90 degrees out of sync leading to destructive interference.
  • One participant proposes a mathematical relationship between phase difference and path difference, suggesting that phase difference can be calculated using the equation phase difference = 2π/λ * path difference.
  • Another participant introduces the concept of optical thickness, discussing how phase varies with distance and refractive index, and notes that the relationship between path and phase difference can become complex under certain conditions.
  • There is a suggestion that under certain circumstances, such as when discussing rays, path and phase difference may not be distinct, but this is contingent on specific conditions like light focusing and polarization.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between path difference and phase difference, with some suggesting they are equivalent under certain conditions while others highlight complexities that arise in specific scenarios. The discussion remains unresolved regarding the nuances of these concepts.

Contextual Notes

Participants acknowledge that variations in refractive index and wave focusing can complicate the relationship between path and phase difference, indicating that assumptions about uniformity may not hold in all cases.

Fuego
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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 receive the crest and the other ear receive 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.
 
bootsam said:
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 receive the crest and the other ear receive 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
 
As a beam traverses space, the phase of a ray goes as [tex]\phi (z) = k n z[/tex], 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.

Even so, there is no difference between path and phase difference, when you are able to sensibly speak of rays. This is not always the case- strongly focused light, for example. Simply considering polarization can create difficulties, forcing you to keep track of the propagation axes by hand.
 

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