# Determine the radius of curvature of a Plano-convex or a bi-convex Lens by Newton’s Rings.

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## Abstract

It well known that radius of curvature of a Plano-convex or  Bi-convex lens can be determined using Newton’s Rings set up making use of Interference by division of amplitude principle. The general method widely used involves measurement of diameter of several circular dark fringes. The method use simpler geometry and the formulae are easier to derive. We present the experimental data. The results from the experiment are in agreement with results obtained through the general method.

## Introduction

It is well known Newton described the formation of bright and dark rings using the Plano-convex lens . It is understood that when a monochromatic beam of light falls normally on a Planoconvex lens kept on an optically plane glass plate, concentric bright and dark circular fringes are formed due to the constructive and destructive interference of light waves reflected from the lower surface of the lens and the upper surface of the plane glass plate. Formation of a bright or dark fringe at a point depends on the thickness of the air film at that point (which creates path difference). Conventionally Newton’s rings experiment is used to determine the radius of curvature of a Plano-convex lens. The general method widely used involves measurement of the diameter of several fringes.

Newton's rings is a phenomenon in which an interference pattern is created by the reflection of light between two surfaces—a spherical surface and an adjacent touching flat surface. It is named for Isaac Newton, who first studied the effect in 1717. When viewed with monochromatic light, Newton's rings appear 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 .

Plano-convex lenses are positive focal length elements that have one spherical surface and one flat surface. These lenses are designed for infinite conjugate (parallel light) use or simple imaging in non-critical applications. These optic lenses are ideal for all-purpose focusing elements .
Bi-convex lens are the simple lenses which comprises of two convex surfaces in spherical form, generally having the same kind of radius of curvature. These are also called as convexconvex lens .
A spherical lens or mirror surface has a center of curvature located in (x, y, z) either along or decentered from the system local optical axis. The vertex of the lens surface is located on the local optical axis. The distance from the vertex to the center of curvature is the radius of curvature of the surface .

## Theory

When a Plano-convex lens of long focal length is placed over an optically plane glass plate, a thin air film with varying thickness is enclosed between them. The thickness of the air film is zero at the point of contact and gradually increases outwards from the point of contact. When the air film is illuminated by monochromatic light normally, alternate bright and dark concentric circular rings are formed with dark spot at the centre. These rings are known as Newton’s rings .
Setting up the Newton’s rings, the diameter of 1st, 3rd, 5th, 9th  and 11th dark fringes are calculated. If Dn+p and Dn represent the diameter of the (n+p)th and nth dark fringe, the radius of curvature is determined using the formula,

Where,
Dn= Diameter of nth ring.
Dn+p= Diameter of (n+p)th ring.
λ = Wavelength of sodium light.

## Calculation

Mean wavelength of sodium light (λ) = 5893 The radius of curvature of the lower surface of the given Lens = 57.27134 cm

## Percentage of Error

Here, the standard result is 65 cm.

## Result

The radius of curvature of the given lens is found to be = 57.27134 Cm with error of 11.89%

## Discussion

Determine the radius of curvature of a Plano-convex or a Biconvex lens by Newton’s rings is an easy process to determine the radius of curvature of lens. But at first time we had to face some difficulties and problems to run the experiment.
The intensity of the ring system decreases as one goes from the inner to the outer rings, thus setting a limit for the selection of the outermost ring whose diameter is to be measured.
Newton’s rings was also observed in transmitted light but in that case the rings was less clearly defined and less suited for measurement.
The first few rings near the centre was deformed due to various reasons. The measurement of diameters of these rings was avoided.
The inner rings were somewhat broader than the outer ones.
Here some error was introduced while measuring the diameter.
For avoiding these errors we have to maintain some precautions. Those are-
(1) Glass plates and lens should be cleaned thoroughly.
(2) The Plano-convex lens should be of large radius of curvature.
(3) The sources of light used should be an extended one.
(4) The range of the microscope should be properly adjusted before measuring the diameters.
(5) Crosswire should be focused on a dark ring tangentially.
(6) The centre of the ring system should be a dark spot.
(7) The microscope is always moved in the same direction to avoid back lash error.
(8) Radius of curvature should be measured accurately.

## Conclusion

It is well known Newton described the formation of bright and dark rings using the Plano-convex lens . It is understood that when a monochromatic beam of light falls normally on a Planoconvex lens kept on an optically plane glass plate, concentric bright and dark circular fringes are formed due to the constructive and destructive interference of light waves reflected from the lower surface of the lens and the upper surface of the plane glass plate. Formation of a bright or dark fringe at a point depends on the thickness of the air film at that point (which creates path difference). Conventionally Newton’s rings experiment is used to determine the radius of curvature of a Plano-convex lens. The general method widely used involves measurement of the diameter of several fringes.

## References

 Ajoy Ghatak, 1991, Optics ,Tata Mcgraw Hill publication, 3rd Edition, 13.16
 Chattopadhyay, 2002, An advanced course in Practical  Physics, Central Publication, 6th Edition, 227
 https://en.wikipedia.org/wiki/Newton%27s_rings
 https://escooptics.com/collections/plano-convex
 http://byjus.com/physics/biconvex-lens/