# Newton's rings

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Newton's rings
Newton's Rings observed through a microscope. The smallest increments on the superimposed scale are 100μm.
The experimental setup: a convex lens is placed on top of a flat surface.

The phenomenon of Newton's rings, named after Isaac Newton who first studied them in 1717, is an interference pattern caused by the reflection of light between two surfaces - a spherical surface and an adjacent flat surface. When viewed with monochromatic light 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 wavelengths 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

$r_N= \left[\left(N - {1 \over 2}\right)\lambda R\right]^{1/2},$

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 in his 1664 book Micrographia although its name derives from the physicist Isaac Newton, who was the first to analyze it.

• NOTE: The above formula is applicable only for Newton's rings obtained by reflected light.
Newton's rings seen in two plano-convex lenses with their flat surfaces in contact. One surface is slightly convex, creating the rings. In white light the rings are rainbow-colored because the different wavelengths of each color interfere at different locations.

## 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 reflectedThe 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 R2 = R2 − 2Rt + t2 + x2

2Rt = t2 + x2

t < < x so t2 < < < x2 therefore:

$2t = {X^2 \over R}$ and finally, we have:

$t = {X^2 \over 2R}$

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### Look at other dictionaries:

• Newton's rings — n pl colored rings due to light interference that are seen about the contact of a convex lens with a plane surface or of two lenses differing in curvature …   Medical dictionary

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• Newton's rings — Optics. the pattern of light interference produced by the contact of the convex surface of a lens with a plane glass plate, appearing as a series of concentric, alternately bright and dark rings, which are colored if the light source is white.… …   Universalium

• Newton's rings — /ˈnjutnz rɪŋz/ (say nyoohtnz ringz) plural noun coloured concentric rings which are produced by interference of light round the point of contact of a convex lens and a plane reflecting surface. {named after Sir Isaac Newton} …   Australian English dictionary

• newton's rings — noun plural Usage: usually capitalized N : colored rings due to light interference that are seen about the contact of a convex lens with a plane surface or of two lenses differing in curvature …   Useful english dictionary

• Newton's rings — plural noun Optics circular interference fringes seen around the point of contact of a convex lens and a plane surface …   English new terms dictionary

• Newton, Sir Isaac — born Jan. 4, 1643, Woolsthorpe, Lincolnshire, Eng. died March 31, 1727, London English physicist and mathematician. The son of a yeoman, he was raised by his grandmother. He was educated at Cambridge University (1661–65), where he discovered the… …   Universalium

• Newton , Sir Isaac — (1642–1727) English physicist and mathematician Newton s father, the owner of the manor of Woolsthorpe in Lincolnshire, died three months before Newton was born. The family had land but were neither wealthy nor gentry. Left by his mother in the… …   Scientists