You probably didn't find much because you were searching on the wrong term. The phenomenon isn't commonly called 'The Newton Effect,' it's usually called 'Newton's Rings.'
Briefly, Newton's Rings are an optical property of physics that occurs between two pieces of glass when one piece of glass is convex and the other piece is flat and there is airspace between the two elements. Due to the particular way that that light waves diffract as they transition between the convex glass element and the air between the glass elements, a series of concentric light and dark colored rings can occur. As I spend my time trying to avoid the effect, I don't have a good picture of it occurring that I can share myself, but a picture of this phenomenon 'in action' can be found here...
Newton's Rings can occur in any optics application that involves combining convex, flat glass elements, and air, but the 3 areas that are most applicable on photo.se.com are:
Photography: Sometimes you can cause Newton's Rings to occur when taking pictures by placing a filter in front of the lens (flat surface of the filter, convex surface of the first lens element). I have the most 'luck' in producing them when I'm shooting at night and pointing at bright things (street lamps, the moon, etc.) Often I can 'make' the phenomenon happen 'before my very eyes' by using a circular filter and rotating it slowly until the rings appear. My recommendation (which is blasphemy in some circles) is to not put filters on your camera unless you are doing it for a specific reason. In other words... Ditch the cheap UV filter.
Darkroom work: This seems to be 'enlarger specific,' and while I can make some enlargers produce this effect consistently, others I can't ever get it to happen. Most of the time the effect will occur at the extreme ends of the enlargers zoom range, and it is more likely to occur with medium or large format negatives (because a larger negative is more likely to have a warp/convex shape to it) and/or when using a glass negative carrier. My recommendations are to not crank your enlarger in or out to its extremes, and if necessary/possible, eliminate the glass negative carrier.
Scanning: If a film negative is in contact with the glass in a bed scanner, and there is a curl in the negative (again, more common with medium and large format negatives), this can cause Newton's Rings on a scan. Additionally, if the neg is in a glass carrier it can cause the phenomenon as well. This is where 'anti-Newton glass' can come into play. For scans where anti-Newton glass doesn't work (it happens), the next step is to eliminate as many layers of glass as you can (if possible), by taking the neg out of its glass holder. It is even possible (although you'll want to seek more expert advice before you carry this out so you don't damage anything) to immerse the negative in solution before scanning it in order to eliminate them.