Which are the rays that form the fringes in wedge shaped film and Newton's rings? While reading interference by the division of amplitude, I came across this doubt. Different sources seem to hint towards different answers. First, in wedge-shaped film, in the book Optics by Ajoy Ghatak, p210, considering an extended source, the formation of fringes on the wedge is schematically shown by the following diagram.

But, while reading Optics by Hecht, 5th edition, for the same condition, this is the diagram given (p421).

In the above diagrams, the formation of the fringes at the top of the wedge, when seen through the naked eye seems to happen for different reasons. In the first image, two different rays originating from the same point on the extended source seem to interfere at a point on the wedge and later pass through the eye. When the eye is focused at that point, the rays will recombine on the retina and hence appear bright or dark depending on the thickness of the film at the point on the wedge.
In the second image, a single ray from the extended source alone seems to be responsible for the formation of the bright or dark fringe at that point on the wedge, if the eye is focused such that the two reflected rays from the incident ray recombine on the retina. Also, while looking for other sources, even this website seems to agree with the second image since they calculate path difference between rays reflected from the same incident rays indicating that the reflected rays will lead to the formation of the fringe when they recombine on the retina.
The same doubt is carried to Newton's rings case. Are the rings we see through the traveling microscope formed by the reflected rays of the same incident ray or by different incident rays which are very close to each other? Are the two cases infact different depending upon where our eyes are focused?
Thank you!
 A: This is a very good question which can have a relatively simple answer in some cases but is much more difficult to answer in other cases.
To simplify my analysis I have ignored the refraction of rays as they pass though an air/glass interface and any phase changes at these interfaces.
When dealing with wedge fringe localisation many textbooks have diagrams which look like those below.

These diagrams are illustrate to show that the real (left-hand diagram) and virtual (right-hand diagram) fringes are localised near the wedge where the rays cross.
As you have pointed out only one incoming ray is shown and hence only one point of intersection where the waves overlap.
Another way of discussing wedge fringes produced by a point source is shown below.

The point source produces two virtual images which act as two coherent sources and where the waves from those two sources overlap there is interference.
I have only shown by shading a limited region where there is interference.
This shows that in this case the fringes are non-localised just like the ones for Young's double slits.
This means that they can be viewed wherever the waves from the two sources overlap.
An important part of the fringe system is the zero order where the path difference form the two virtual sources to some point $x$ is the same, $a'X = a''X$.
Now what happens when a second point source is used as in the left-hand diagram below?

There are now two overlapping interference patterns produced by virtual sources $a'\,a''$ and $b'\,b''$ which might mean that fringes are no longer visible.
However out of the chaos there is a region around $Y$ where the zero order fringes of the two patterns overlap.
If one then focusses on this region one would see fringes.
These are the localised fringes near the wedge.
Moving on and adding a third point source and then to even more which is equivalent to having an extended source you will note in the right hand diagram the zero order fringes being roughly in the same area.
The visibility of the zero order and adjacent order fringes improves if one observed the fringes from positions normal to the wedge and again the fringes are localised near the wedge ie to see the fringes you must focus on a region near the apex of the wedge.
An experimental arrangement is shown below with the microscope, which has a very small depth of field, focussed on the wedge.

