# Newton's Rings

## Newton's rings are a series of concentric circles centered at the point of contact between a spherical and a flat surface.

#### Key Points

• When viewed with monochromatic light, Newton's rings appear as alternating bright and dark rings; when viewed with white light, a concentric ring pattern of rainbow colors is observed.

• If the path length difference between the two reflected light beams is an odd multiple of the wavelength divided by two, λ/2, the reflected waves will be 180 degrees out of phase and destructively interfere, causing a dark fringe.

• If the path length difference is an even multiple of λ/2, the reflected waves will be in-phase with one another. The constructive interference of the two reflected waves creates a bright fringe.

#### Terms

• The length of a single cycle of a wave, as measured by the distance between one peak or trough of a wave and the next; it is often designated in physics as λ, and corresponds to the velocity of the wave divided by its frequency.

• an object, usually made of glass, that focuses or defocuses the light that passes through it

• Describes a beam of light with a single wavelength (i.e., of one specific color or frequency).

#### Figures

1. ##### Newton's Rings in a drop of water

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.

2. ##### Formation of Interference Fringes

This figure shows how interference fringes form.

## Newton's Rings

In 1717, Isaac Newton first analyzed an interference pattern caused by the reflection of light between a spherical surface and an adjacent flat surface. Although first observed by Robert Hooke in 1664, this pattern is called Newton's rings, as Newton was the first to analyze and explain the phenomena. Newton's rings appear as a series of concentric circles centered at the point of contact between the spherical and flat surfaces. When viewed with monochromatic light, Newton's rings appear as alternating bright and dark rings; when viewed with white light, a concentric ring pattern of rainbow colors is observed. An example of Newton's rings when viewed with white light is shown in the figure below (Figure 1).

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. The outer rings are spaced more closely than the inner ones because the slope of the curved lens surface increases outwards. The radius of the Nth bright ring is given by:

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

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.

A spherical lens is placed on top of a flat glass surface. An incident ray of light passes through the curved lens until it comes to the glass-air boundary, at which point it passes from a region of higher refractive index n (the glass) to a region of lower n (air). At this boundary, some light is transmitted into the air, while some light is reflected. The light that is transmitted into the air does not experience a change in phase and travels a a distance, d, before it is reflected at the flat glass surface below. This second air-glass boundary imparts a half-cycle phase shift to the reflected light ray because air has a lower n than the glass. The two reflected light rays now travel in the same direction to be detected. As one gets farther from the point at which the two surfaces touch, the distance d increases because the lens is curving away from the flat surface (Figure 2).

If the path length difference between the two reflected light beams is an odd multiple of the wavelength divided by two, λ/2, the reflected waves will be 180 degrees out of phase and destructively interfere, causing a dark fringe. If the path-length difference is an even multiple of λ/2, the reflected waves will be in phase with one another. The constructive interference of the two reflected waves creates a bright fringe.

#### Key Term Glossary

constructive interference
Occurs when waves interfere with each other crest to crest and the waves are exactly in phase with each other.
##### Appears in these related concepts:
destructive interference
Occurs when waves interfere with each other crest to trough (peak to valley) and are exactly out of phase with each other.
##### Appears in these related concepts:
incident ray
The ray of light that strikes the surface.
##### Appears in these related concepts:
interfere
(of waves) To be correlated with each other when overlapped or superposed.
##### Appears in these related concepts:
interference
An effect caused by the superposition of two systems of waves, such as a distortion on a broadcast signal due to atmospheric or other effects.
##### Appears in these related concepts:
lens
an object, usually made of glass, that focuses or defocuses the light that passes through it
##### Appears in these related concepts:
light
The natural medium emanating from the sun and other very hot sources (now recognised as electromagnetic radiation with a wavelength of 400-750 nm), within which vision is possible.
##### Appears in these related concepts:
monochromatic
Describes a beam of light with a single wavelength (i.e., of one specific color or frequency).
##### Appears in these related concepts:
phase
Any one point or portion in a recurring series of changes, as in the changes of motion of one of the particles constituting a wave or vibration; one portion of a series of such changes (in distinction from a contrasted portion) as the portion on one side of a position of equilibrium (in contrast with that on the opposite side).
##### Appears in these related concepts:
ray
A line extending indefinitely in one direction from a point.
##### Appears in these related concepts:
reflection
the property of a propagated wave being thrown back from a surface (such as a mirror)
##### Appears in these related concepts:
refractive index
The ratio of the speed of light in air or vacuum to that in another medium.
##### Appears in these related concepts:
series
A number of things that follow on one after the other or are connected one after the other.
##### Appears in these related concepts:
wave
A moving disturbance in the energy level of a field.
##### Appears in these related concepts:
wavelength
The length of a single cycle of a wave, as measured by the distance between one peak or trough of a wave and the next; it is often designated in physics as λ, and corresponds to the velocity of the wave divided by its frequency.