Newton's rings

Newton's rings is a phenomenon in which an interference pattern is created by the reflection of light between two surfaces—a spherical surface and an adjacent touching flat surface. It is named for Isaac Newton, who investigated the effect in his 1704 treatise Opticks. When viewed with monochromatic light, Newton's rings appear as a series of concentric, alternating bright and dark rings centered at the point of contact between the two surfaces. When viewed with white light, it forms a concentric ring pattern of rainbow colors, because the different wavelengths of light interfere at different thicknesses of the air layer between the surfaces. Newton's rings is a phenomenon in which an interference pattern is created by the reflection of light between two surfaces—a spherical surface and an adjacent touching flat surface. It is named for Isaac Newton, who investigated the effect in his 1704 treatise Opticks. When viewed with monochromatic light, Newton's rings appear as a series of concentric, alternating bright and dark rings centered at the point of contact between the two surfaces. When viewed with white light, it forms a concentric ring pattern of rainbow colors, because the different wavelengths of light interfere at different thicknesses of the air layer between the surfaces. The phenomenon was first described by Robert Hooke in his 1664 book Micrographia, although its name derives from the physicist Sir Isaac Newton, who was the first to analyze it. The pattern is created by placing a very slightly convex curved glass on an optical flat glass. The two pieces of glass make contact only at the center, at other points there is a slight air gap between the two surfaces, increasing with radial distance from the center. The diagram at right shows a small section of the two pieces, with the gap increasing right to left. Light from a monochromatic (single color) source shines through the top piece and reflects from both the bottom surface of the top piece and the top surface of the optical flat, and the two reflected rays combine and superpose. However the ray reflecting off the bottom surface travels a longer path. The additional path length is equal to twice the gap between the surfaces. In addition the ray reflecting off the bottom piece of glass undergoes a 180° phase reversal, while the internal reflection of the other ray from the underside of the top glass causes no phase reversal. The brightness of the reflected light depends on the difference in the path length of the two rays: This interference results in a pattern of bright and dark lines or bands called 'interference fringes' being observed on the surface. These are similar to contour lines on maps, revealing differences in the thickness of the air gap. The gap between the surfaces is constant along a fringe. The path length difference between two adjacent bright or dark fringes is one wavelength λ of the light, so the difference in the gap between the surfaces is one-half wavelength. Since the wavelength of light is so small, this technique can measure very small departures from flatness. For example, the wavelength of red light is about 700 nm, so using red light the difference in height between two fringes is half that, or 350 nm, about 1/100 the diameter of a human hair. Since the gap between the glasses increases radially from the center, the interference fringes form concentric rings. For glass surfaces that are not spherical, the fringes will not be rings but will have other shapes. For illumination from above, with a dark center, the radius of the Nth bright ring is given by where N is the bright-ring number, R is the radius of curvature of the glass lens the light is passing through, and λ is the wavelength of the light.