Circular fringes, also known as Newton's rings, are produced in Michelson interferometers when a plano-convex lens is placed on a flat glass plate. These fringes result from the interference of light waves reflected from the top and bottom surfaces of the air gap between the lens and the glass plate.
When monochromatic light is incident on the lens, part of it is reflected from the top surface of the air gap, while the rest passes through the air gap and is reflected from the bottom surface of the air gap. These two reflected waves then combine and interfere with each other, creating a pattern of alternating bright and dark rings.
The circular shape of the fringes arises from the variation in the thickness of the air gap across the surface of contact between the lens and the glass plate. The thickness of the air gap determines the phase difference between the reflected waves, and this phase difference leads to constructive or destructive interference at different points.
At the center of the contact region, where the air gap is thinnest, the path lengths of the two waves are nearly equal, resulting in constructive interference and a bright spot. As you move away from the center, the thickness of the air gap gradually increases, leading to a progressive phase difference between the waves. This phase difference causes the interference pattern to change, resulting in a series of concentric bright and dark rings.
The spacing between the rings depends on the wavelength of light used and the curvature of the lens. By analyzing the pattern of circular fringes, one can gather information about the curvature of the lens or the flatness of the glass plate. This phenomenon is widely used in interferometry for precise measurements and quality control purposes.