Interference pattern from a plano-concave lens

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Hello. I need some sort of explanation. I was unsuccessfully trying to find information on the web and derivation by hand seems rather complicated for me. So I have a such set-up:

HeNe laser ->> plano-concave lense )], light is incident by some angle (NON 0°). then looking to reflection screen I clearly see two reflections and one of them (smaller) having clear Newton's rings pattern. As I understand it is interference between the first surface (concave) and the second surface (plane) reflections. My question is: can I somehow determine RoC from this pattern (attached)?

The pattern seems to be sensitive to orientation and position of the lens.
 

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i had the problem for some time too
the key is to realize that the lens is not just two dimensional circle if that was the case what you said about forming straight line interference would be true but the lens used in the Newton ring experiment is a three dimensional spherical lens so you can imagine the central dark spot as being the point of the sphere that is tangent to the plane and the all the other points which are of the same height from the plane as forming those dark rings hope this helps sorry for the very very late reply