Newton's Rings

3D Physics Simulation

Newton's Rings

3D Light Interference Simulation
Plano-Convex Lens Transparent curved glass surface
Glass Plate Flat optical glass surface
Air Film Thin gap between lens & plate
Interference Rings Newton's ring pattern
Light Source Monochromatic lamp
Light Rays Incoming & reflected beams
Theory
⚛ Lab Controls
Wavelength 550 nm
Green Light
Radius of Curvature 100 cm
Film Thickness 1.0 ×
📚 Physics Guide

What are Newton's Rings?

Concentric interference fringes formed when monochromatic light reflects between a plano-convex lens and a flat glass plate separated by a thin air film of gradually increasing thickness.

Why Interference?

Ray 1 reflects at the glass-air boundary (no phase shift). Ray 2 reflects at the air-glass boundary gaining a π phase shift. Their superposition creates bright and dark rings.

Dark Ring Formula

rₙ = √(n · λ · R)

n = ring order  •  λ = wavelength  •  R = radius of curvature
The centre is always dark (phase reversal).

Key Physics

• Shorter λ → rings crowd together
• Larger R → rings spread outward
• Air gap: t = r² / 2R
• Dark rings: 2t = nλ

Live Measurements

1st Dark Ring
—
5th Dark Ring
—
10th Dark Ring
—
Visible Rings
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Stage 0 • Setup
Press Start to begin the experiment.
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What are Newton's Rings?

Newton's Rings is a phenomenon of light interference observed when a plano-convex lens is placed on top of a flat glass plate. When monochromatic light falls on this arrangement, a series of concentric bright and dark rings is observed around the point of contact. These rings are formed due to the interference between the light waves reflected from the lower surface of the lens and the upper surface of the glass plate, with the thin air film trapped between them acting as the medium of interference.

This phenomenon was first observed and described by Sir Isaac Newton in 1717, and it provides a classic demonstration of wave optics. The pattern of rings reveals fundamental properties of light, particularly its wave nature, and is used practically to measure the radius of curvature of lenses and to test the optical flatness of surfaces.

rₙ = √(n · λ · R)
The above formula gives the radius of the nth dark ring, where n is the ring order, λ is the wavelength of light, and R is the radius of curvature of the lens. The centre of the pattern is always dark due to a phase reversal upon reflection.

Principle of Interference

The formation of Newton's Rings is based on the principle of thin film interference. When a ray of monochromatic light falls on the air film between the lens and the glass plate, it splits into two rays: one reflected from the bottom surface of the lens (glass-to-air boundary) and another transmitted through the air film and reflected from the top surface of the glass plate (air-to-glass boundary). The second ray undergoes a phase change of π (180°) upon reflection because it travels from a rarer medium (air) to a denser medium (glass).

These two reflected rays travel back and recombine. Where their path difference satisfies the condition for destructive interference (path difference = nλ), a dark ring appears. Where the condition for constructive interference is met (path difference = (2n−1)λ/2), a bright ring appears. Since the air gap thickness increases radially outward from the point of contact, the rings appear at increasing radii, but become progressively closer together as their spacing follows a square-root relationship.

Components of the Newton's Rings Experiment

  • Plano-Convex Lens: A lens with one flat and one convex surface. Its curved surface rests on the glass plate, creating an air wedge of gradually increasing thickness. The radius of curvature R determines the spacing of the rings.
  • Flat Glass Plate: A polished optically flat glass surface placed below the lens. It provides the second reflecting surface and must be smooth to produce clear, distinct rings.
  • Air Film: The thin layer of air trapped between the curved surface of the lens and the flat glass plate. The thickness of this air film increases from zero at the point of contact outward, producing the ring pattern.
  • Monochromatic Light Source: A light source emitting a single wavelength, such as a sodium lamp (589 nm) or a laser. Monochromatic light is essential for producing sharp, well-defined rings; white light produces coloured rings with poor contrast.
  • Glass Plate (Beam Splitter): An inclined glass plate at 45° that reflects the incident light downward onto the lens-plate arrangement, directing the monochromatic beam vertically downward for normal incidence.
  • Travelling Microscope: A precision instrument used to observe and measure the diameters of the Newton's Rings. It can move along horizontal and vertical axes with micrometer accuracy.
  • Interference Rings: The concentric circular fringes formed on the surface of the glass plate. The diameters of successive dark rings are used to calculate the radius of curvature of the lens and, if the radius is known, the wavelength of light.
  • Point of Contact (Centre): The point where the lens just touches the glass plate. The air film thickness here is theoretically zero, yet the centre appears dark because the reflection at the air-glass interface introduces a half-wavelength phase shift.

Mathematical Analysis

For a plano-convex lens of radius of curvature R, the thickness of the air film at a radial distance r from the point of contact is given by t = r² / 2R. The condition for the nth dark ring (destructive interference, accounting for the π phase shift) is 2t = nλ, which gives r⊂n;² = nλR. Therefore the radius of the nth dark ring is rn = √(nλR).

The diameter of the nth dark ring is Dn = 2rn = 2√(nλR). A practical formula used in the laboratory to determine either the radius of curvature or the wavelength is derived from the difference of squares of ring diameters:

R = (Dₙ² − Dₓ²) / (4(n − m)λ)

This relationship eliminates the error arising from the difficulty of locating the exact centre of the ring pattern, and is the standard method used in optical laboratories. By measuring the diameters of several rings and plotting Dn² against n, a straight line is obtained whose slope equals 4λR, enabling accurate determination of R or λ.

Applications of Newton's Rings

Newton's Rings have significant practical applications in optical science and engineering. The most common application is the precise measurement of the radius of curvature of lenses and curved optical surfaces, which is essential in lens manufacturing and quality control. By using a known wavelength of light, the radius R can be calculated accurately from ring diameter measurements.

Conversely, if the radius of curvature is known, Newton's Rings can be used to determine the wavelength of an unknown monochromatic light source. In optical workshops, Newton's Rings are used to test the flatness of optical surfaces — a perfect flat surface in contact with a reference flat produces perfectly circular, evenly spaced rings, while any deviation from flatness distorts the ring pattern. This technique is used in the manufacture of telescope mirrors, camera lenses, and precision optical instruments.

Key Takeaway: Newton's Rings provide a direct, elegant demonstration that light behaves as a wave. The concentric ring pattern arises entirely from wave interference in the thin air film. The mathematical simplicity of the formula rn = √(nλR) makes this experiment one of the most precise and reproducible methods in classical optics for measuring curvature and wavelength, and it remains a cornerstone of undergraduate physics laboratories worldwide.