Newton’s Rings

Definition

Newton’s rings are the concentric circular bright and dark fringes formed due to interference of light reflected between the lower surface of a plano-convex lens and the upper surface of a plane glass plate when monochromatic light is incident on the system.

Main Content

1. Interference of Light in Thin Films

• Newton’s rings are produced because the air film between the lens and the glass plate acts as a thin film of varying thickness.
• Light reflected from the top and bottom surfaces of this thin air film interferes, and the nature of interference depends on the film thickness at each point.

At the point of contact, the thickness of the air film is zero and increases gradually as we move away from the center. Because the film thickness changes radially, the path difference between the two reflected rays also changes from point to point, producing circular fringes. This is why the rings are concentric and centered at the point of contact. The pattern is a classic example of thin-film interference and is commonly studied in experiments using sodium light or another monochromatic source.

2. Formation of Bright and Dark Rings

• Dark rings are formed when the reflected rays undergo destructive interference.
• Bright rings are formed when the reflected rays undergo constructive interference.

In reflected light, one of the rays undergoes a phase change of 180° because reflection occurs from a denser medium. This phase reversal is crucial in determining the conditions for minima and maxima. For the air film, the condition for a dark ring is typically satisfied when the path difference leads to destructive interference, and the center appears dark because the thickness is zero there. The first few rings are closely spaced near the center and become farther apart as the radius increases. In transmitted light, the nature of the pattern is reversed: bright rings in reflected light correspond to dark regions in transmitted light, and vice versa.

3. Mathematical Relationship and Measurement

• The radius of the nth dark ring is related to the wavelength of light and the radius of curvature of the lens.
• Newton’s rings can be used to determine physical quantities such as wavelength, refractive index, and lens curvature.

For a plano-convex lens of radius of curvature $R$, the thickness of the air film at a distance $r$ from the center is approximately $t = \frac{r^2}{2R}$. For reflected light, the condition for dark rings is:

$$2t = n\lambda$$

Substituting the expression for $t$, we get:

$$r_n^2 = n\lambda R$$

where $r_n$ is the radius of the nth dark ring, $n$ is the ring order, $\lambda$ is the wavelength of light, and $R$ is the radius of curvature of the lens. This formula is extremely useful because by measuring ring diameters, one can calculate the wavelength of light or the curvature radius of the lens with good precision. If a liquid is introduced between the lens and plate, the ring size changes depending on the liquid’s refractive index, making the method useful for refractive index determination.

Working / Process

1. A plano-convex lens is placed on a flat glass plate so that a thin air film is formed between them.
2. Monochromatic light is directed normally onto the lens-plate system, and the reflected light is observed through a microscope or viewing device.
3. Due to interference in the thin film, alternating bright and dark concentric rings appear; their radii are measured to determine wavelength, refractive index, or lens curvature.

Advantages / Applications

• Newton’s rings provide a simple and accurate demonstration of interference and the wave nature of light.
• They are used to determine the wavelength of monochromatic light, especially in laboratory experiments.
• They help in measuring the radius of curvature of a plano-convex lens and the refractive index of liquids placed between the surfaces.
• They are also useful for testing the quality and flatness of optical surfaces in precision optics.

Summary

• Newton’s rings are concentric interference fringes produced by a thin air film between a lens and a glass plate.
• The pattern is formed due to constructive and destructive interference of reflected light.
• The ring radii depend on wavelength, refractive index, and the radius of curvature of the lens.
• Newton’s rings are an important experimental proof of the wave nature of light.