The Double Slit Interference: How does it relate to the definition of coherence?

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Discussion Overview

The discussion revolves around the concept of coherence in the context of double slit interference patterns. Participants explore the relationship between coherence, phase differences, and the resulting interference fringes observed on a screen. The conversation touches on foundational concepts relevant to wave behavior and interference, aimed at clarifying the definition and implications of coherence.

Discussion Character

  • Conceptual clarification
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant questions the definition of coherence, noting that while coherent waves are said to have a constant phase difference, the phase difference changes at different points on the screen, leading to confusion.
  • Another participant clarifies that the "constant phase difference" refers to the difference between the two waves arriving at a specific point on the screen, suggesting that this phase difference can vary from point to point.
  • A follow-up response confirms that the phase difference at a specific point is influenced by both the original phase difference between the sources and the additional phase difference due to path differences.
  • Mathematical representation of the phase difference is provided, indicating how it is calculated based on path differences and wavelength.

Areas of Agreement / Disagreement

Participants generally agree on the clarification of how phase differences work in relation to coherence and interference patterns. However, the initial confusion regarding the definition of coherence and its implications remains a point of discussion.

Contextual Notes

The discussion does not resolve the initial participant's confusion about coherence, indicating a potential gap in understanding the relationship between phase differences and coherence in the context of interference patterns.

PFuser1232
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I know this is a very trivial concept, so can someone please point out to me where I'm going wrong with this? We use coherent waves to observe an interference pattern, and coherence by definition is the presence of a constant phase difference between two waves. Yet, we see bright and dark fringes, and at each fringe the phase difference between the two waves is different. Doesn't this contradict the definition of coherence? Where am I getting this wrong?
By the way, I'm still in high school, so I would not be able to understand any discussions regarding wave functions and quantum mechanics.
 
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When we say "constant phase difference between two waves" we mean "between the waves along the two paths from the two sources to a particular point on the screen."

Call the two sources A and B, and call points on the screen 1, 2, etc.

The two waves that arrive at point 1 from A and B must have a constant phase difference. The amount of phase difference determines whether point 1 is on a bright fringe, a dark fringe, or in between.

The two waves that arrive at point 2 from A and B must also have a constant phase difference, but this difference may be a different amount from the difference at point 1.
 
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jtbell said:
When we say "constant phase difference between two waves" we mean "between the waves along the two paths from the two sources to a particular point on the screen."

Call the two sources A and B, and call points on the screen 1, 2, etc.

The two waves that arrive at point 1 from A and B must have a constant phase difference. The amount of phase difference determines whether point 1 is on a bright fringe, a dark fringe, or in between.

The two waves that arrive at point 2 from A and B must also have a constant phase difference, but this difference may be a different amount from the difference at point 1.

Thanks! Makes sense now!
So, let's say the two waves have a phase difference of 0. Would it be appropriate to say that this phase difference changes once the two waves reach a point on the screen? (As a result of the path difference.)
 
Yes. The phase difference at a particular point on the screen comes about in two ways: (a) the original phase difference between the sources, and (b) the additional phase difference caused by the path difference.

If the phase difference (in radians) is δ and the path difference (in meters) is Δ, then
$$\delta = \delta_0 + 2 \pi \frac{\Delta}{\lambda}$$
(one cycle of phase difference = ##2\pi## radians.)
 

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