Newton's rings are circular because of the interference of light waves. When a plano-convex lens is placed on top of a flat glass surface, a thin layer of air is trapped between them. When light is incident on this thin film, some of it is reflected from the top surface of the air film, and some of it is reflected from the bottom surface where the air film meets the glass surface.
These two reflected light waves can interfere constructively or destructively depending on their phase relationship. The interference pattern creates alternating bright and dark rings. The circular shape of the rings is a result of the spherical shape of the lens and the way the interfering light waves propagate.
The circular shape arises because the distance between the lens and the glass surface increases as you move outward from the point of contact. This leads to a variation in the thickness of the air film, and hence a variation in the path length traveled by the reflected light waves. The varying path length causes the interference pattern to form concentric circles.
At the center of the pattern, where the air film is thinnest, the path length difference between the two interfering waves is minimal, resulting in constructive interference and a bright spot. As you move outward, the path length difference increases, leading to alternating bright and dark rings.
Therefore, the circular shape of Newton's rings is a consequence of the interference of light waves occurring at different distances from the point of contact between the lens and the glass surface.