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.)