Would rings still be formed if a plano concave lens is used in place of a plano convex lens in the Newton's ring experiment. The locus of points with the same path difference in case of a plano convex lens is a circle, while I suspect that that shouldn't be the case for a plano concave lens though I don't have a rigorous proof for the same.
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If you are using a conventional light source the chances are that you may not observe Newton's rings in the centre if a plano-concave lens is used.
This is because the largest path differences are at the centre of the lens which might result in a reduced visibility of the fringes at the centre.
The most visible fringes will be around the edge of the lens where it is touching the optical flat and so the path differences are smallest.
Overall you will see a similar pattern to that when a convex lens is used the fringes being contours of equal gap thickness and the separation of the fringes near the edge will be smallest because that is where rate rate of change of gap thickness with position from the centre of the lens is greatest - contours close togther $\Rightarrow$ steep slope.
