Newton's rings
Encyclopedia
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
who first studied them in 1717, is an interference pattern caused by the reflection
Reflection (physics)
Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...
of light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
between two surfaces - a spherical
Sphere
A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...
surface and an adjacent flat surface. When viewed with monochromatic light
Monochrome
Monochrome describes paintings, drawings, design, or photographs in one color or shades of one color. A monochromatic object or image has colors in shades of limited colors or hues. Images using only shades of grey are called grayscale or black-and-white...
it appears 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 wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
s of light interfere at different thicknesses of the air layer between the surfaces. The light rings are caused by constructive interference between the light rays reflected from both surfaces, while the dark rings are caused by destructive interference. Also, the outer rings are spaced more closely than the inner ones. Moving outwards from one dark ring to the next, for example, increases the path difference by the same amount λ, corresponding to the same increase of thickness of the air layer λ/2. Since the slope of the convex lens surface increases outwards, separation of the rings gets smaller for the outer rings. For surfaces which are not convex, the fringes will not be rings but will have other shapes.
The radius of the Nth Newton's bright ring is given by
where
N is the bright ring number, R is the radius of curvature of the lens the light is passing through, and λ is the wavelength of the light passing through the glass.
The phenomenon was first described by Robert Hooke
Robert Hooke
Robert Hooke FRS was an English natural philosopher, architect and polymath.His adult life comprised three distinct periods: as a scientific inquirer lacking money; achieving great wealth and standing through his reputation for hard work and scrupulous honesty following the great fire of 1666, but...
in his 1664 book Micrographia
Micrographia
Micrographia is a historic book by Robert Hooke, detailing the then thirty year-old Hooke's observations through various lenses. Published in September 1665, the first major publication of the Royal Society, it was the first scientific best-seller, inspiring a wide public interest in the new...
although its name derives from the physicist Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
, who was the first to analyze it.
- NOTE: The above formula is applicable only for Newton's rings obtained by reflected light.
Theory
There is light incident on the flat plane of the convex lens which is situated on the optically flat glass surface below, the light passes through the glass lens until it comes to the glass-air boundary, here the light goes from a higher refractive index (n) value to a lower n value. The light passes through this boundary and suffers no phase change. Also at this boundary, some light is transmitted into the air and some light is reflected. The light that is transmitted to the air travels a distance t before it is reflected at the flat surface below, the air-glass boundary causes a half-cycle phase shift because the air has a lower refractive index than the glass. The two reflected rays now travel in the same direction to be detected. The convex lens touches the flat surface below and from this point, as you get further away, the distance t increases because the lens is curving away from the surface
so 
therefore:
and finally, we have: