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

[PFuser1232]

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.

 

[jtbell]

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.

 

[PFuser1232]

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.)

 

[jtbell]

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.)

 

[sardar]

The concept of coherence can be confusing, especially when applied to phenomena like the double slit interference. However, it is important to understand that the definition of coherence applies to the overall behavior of the waves, rather than the specific phase difference at each point.

In the case of the double slit interference, we use coherent waves to observe an interference pattern because they have a constant phase difference over a large distance. This means that the waves maintain their relative positions and amplitudes as they travel, allowing them to interfere constructively or destructively. This is what produces the bright and dark fringes that we observe.

While it may seem that the phase difference at each fringe is different, this is actually due to the interference pattern itself. The waves are still coherent because they maintain their overall constant phase difference over a large distance, which is what allows them to produce the interference pattern.

It is also important to note that the definition of coherence is not limited to just two waves. In the case of the double slit interference, there are actually multiple waves interfering with each other, and their overall coherence is what allows for the interference pattern to be observed.

In summary, the double slit interference does not contradict the definition of coherence. While the specific phase difference at each point may vary, the overall behavior of the waves is still coherent, which is what allows for the interference pattern to be observed.