Lab Experiments

Vol-2, N0-1, June 2002

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Experiment-22 S

NEWTON′′′′S RINGS

Dr S P Basavaraju

Dept. of Physics, Bangalore Institute of Technology, K R Road, Basavanagudi, Bangalore-560004, INDIA

Abstract

The light interference phenomenon is observed as Newton’s Rings. The various optical accessories

used in the observations are studied. A travelling microscope is used to determine the diameter of

the rings. The ring number versus square of the ring diameter plot gives a straight line. From the

slope of the straight line the radius of curvature of the plano-convex lens used for producing

Newton’s rings is determined.

Introduction

Newton’s rings were first observed by Robert Hooke [1]. Sir Isaac Newton provided the relevant

theory based on the wave theory of light in the 17th

century. Light interference is the result of

reinforcement and cancellation of light waves as shown in Figure-1.

Figure-1 a) Two smaller waves with same phase reinforce to get a bigger wave

b) Two waves of equal amplitude and opposite phase collapse on each other and vanish totally

In Figure-1 a) two light waves of equal amplitude and wavelengths add or reinforce to get a wave of

bigger amplitude. In this case the crests of one wave coincide with the crests of the other. Such

reinforcement is called constructive interference. Figure-1 b) indicates that the crests of one wave fall

on the troughs of the other thus canceling each other. Such interference is called destructive

interference Constructive and destructive interferences are responsible for the formation of Newton’s

rings.

To observe Newton’s rings we require an optically plane glass plate and a plano-convex lens as shown

in Figure-2. Over the glass plate the plano-convex lens is placed with its curved surface resting on it.

In the intermediate space between the plate and the lens, an airbed of varying thickness radially and

symmetric around the point of contact, appears to be sandwiched in a plane parallel to the glass plate.

In the airbed, A and B are two equidistant points from the axis OO′of the lens. Each group of such

eqidistance points form a geometrical ring through whose center the axis passes.

+=

=+

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A monochromatic light falling normal to the lens undergoes partial reflection and transmission both at

the curved surface of the lens and at the surface of the glass plate. As a result we will have reflected

rays coming up from every point in the plate and also from every point on the curved surface of the

lens. But each group of light waves coming up from the same geometrical ring will have same phase

difference and will be subjected to same interference condition, either constructive or destructive. The

total visual effect of interference at all the points results in the appearance of Newton’s rings. Light

waves emerging with constructive interference results in bright ring set and since light waves do not

emerge during destructive interference it results in dark ring set. There are light waves emerging with

phase difference other than these two extremes. They contribute to the varying intensity of the ring, i.e.

the intermediate region between maxima of a bright ring to maxima of the next dark ring.

Figure-2, Formation of Newton’s Ring

To observe Newton’s rings the glass plate used should be optically flat and the curvature of the lens

surface should be well uniform. Sometimes the plane glass plate that is given with the lens will also be

circular in shape and may cause confusion. Then, in order to distinguish between the two, they are tried

one by one by holding in front of the eye and shaken sideways while viewing an object through. If it is

the lens, then the image of the object moves, and if it is the plane glass plate then hardly there will be

any movement of the image.

Further, while placing the lens on the glass plate, the lens is kept on the glass plate and given a

rotation. If it rotates freely then it indicates that the curved surface is sitting on the glass plate, which is

the required setting. On the other hand if the attempt to rotate causes jerking movements, it indicates

that the plane surface of the lens is in touch with the glass plate which is not correct.

The Newton’s rings appearing due to either sunlight or fluorescent light is colored. Each ring has an

inner border of red color and outer border of bluish green color. Only 4 to 5 such rings are observed.

These rings can be observed even with the naked eye.

For Newton’s rings obtained from monochromatic light the diameter of the nth ring is given by [2]

dn = √(4Rnλ) …1

.A B

glass plate

. .

O

O

A geometrical ringequidis tance pointsfrom the axia OO

Plano-convex

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where, dn is the diameter of nth ring

R is the radius of curvature of the Plano convex lens

n is the number of the ring

λ is the wavelength of the monochromatic light used

While making use of the above equation for any practical investigation, measurements are generally

carried out on the diameter of the various dark rings. To do the same, a travelling microscope is made

use of. The details of two such travelling microscopes are given in the following discussions.

Newton’s Ring Microscope

(a) (b)

Figure-3, Three Motion Newton’s Ring Microscopes

Instead of using general purpose two motion or three motion travelling microscopes, compact

microscopes that are meant exclusively to observe and make measurements on Newton’s rings are

available. These are called Newton’s ring microscopes. A Newton’s ring microscope has a built in

turning reflector glass plate to reflect a parallel beam of light onto the lens-glass plate assembly.

Figure 3 shows two types of Newton’s ring microscopes. Both are three motion microscopes. The

optical parts are detachable to identify the lens and glass plate. Both the lens and the glass plates are

placed within the lens holder. Then they are covered with a hollow circular cap. The whole assembly is

held together in one microscope by using screws (Figure-3b) and in another (Figure3a) rotating the

cap. Figures 4 shows the optical accessories, the plano-convex lens, and the glass plate. When using

these microscopes, the sodium vapor lamp must be kept close to the microscope (at a distance of about

a foot). This allows the light to focus on to the reflector glass plate.

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Figure –4 Bottom Portion of Newton’s Ring

Figure 5 shows anther type of optical accessories, which is used along with general-purpose

microscope. While using this set-up sodium vapor lamp is kept at a distance of 2 to 3 ft away from the

microscope. The optical accessories shown in Figures 4 and 5 are generally called as bottom portion of

Newton’s ring apparatus. When the bottom portion shown in Figure 4 is made use of, the center dark

spot of the Newton’s rings can be made clearer by adjusting the screws of the mount of lens assembly..

This provision is not available in the bottom portion shown in Figure 5.

Figure –5, 45-degree reflector

Radius of Curvature Determination

Knowing the wavelength of monochromatic light used, and measuring the diameter of a set of dark

rings the radius of curvature of the lens can be determined. The accuracy of the result depends on the

accuracy of measurement of the diameter. While measuring the diameter, the cross wire is placed at the

center of the fringe. If X is the thickness of the fringe then the maximum error involved in the

measurement will be X/2. This may occur when adjusting the cross wire to the edge of the fringe

instead of center of the fringe. This is particularly important for the first few rings, as their fringe

thickness is quite large.

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Apparatus Used

A Newton’s ring microscope set with three motion travelling microscope, a circular glass plate of

45mm dia, plano convex lens of about 250cm radius of curvature, glass reflector, and 35 Watt sodium

vapor lamp.

Experimental Procedure

1. The circular glass plate and the plano-convex lens are identified and the plano-convex lens is

placed above the glass plate with its convex surface resting on the glass plate. The assembly is then

placed inside the cup of the bottom portion and its cap is inserted.

2. The light from a sodium vapor lamp is reflected on the lens assembly by orienting the turning glass

plate to 45-degree inclination to the incident light. This gives a bright illumination in the field of

view in the microscope. Then by moving the microscope to the focusing height above the lens, the

Newton’s rings become visible. If the center of the ring system is not dark, then the cap of the cup

(or the screws) is adjusted to a proper grip until the center dark ring is observed.

3. By operating the head scale drum the intersection of the cross wire is made to coincide with the

center of the ring system which is a dark patch. The eyepiece is rotated to make one of the cross-

wires align in the direction parallel to the scale of the travelling microscope.

4. By rotating the head scale drum, the cross-wires are moved towards to the left from the center

while counting the ordinal number of only the dark rings, till the 12th

ring is reached. Now,

reversing the direction of rotation the cross wire is coincided with the 10th

ring and the microscope

reading is noted in Table-1.

5. Continuing in the same way the cross wire is coincided with the left side of the 9th

, 8th

rings, up to

the 1st ring and the reading corresponding to each is noted in Table-1.

6. Now the readings corresponding to first ring on the right side of ring pattern is noted and recorded

in Table-1. This is continued till the 10th

ring on the right side.

7. By taking the difference of microscope readings of the respective rings from the left side and right

side readings in Table-1, the diameter d of the rings are calculated.

8. A graph is drawn taking square of the diameter on the Y-axis and ring number on the X-axis as

shown in Figure-6. From the straight-line graph the slope is calculated and radius of curvature is

determined by making use of the equation

Slope

R = ----------- …2

4λ

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Table-1

Ring

Number

Microscope Reading Diameter d

(mm)

d2(mm

2)

Left Right

10 40.45 48.02 7.57 57.30

9 40.68 47.95 7.27 52.85

8 40.85 47.76 6.91 47.74

7 41.02 47.61 6.59 43.42

6 41.20 47.37 6.17 38.06

5 41.30 46.42 5.12 26.21

4 41.57 46.12 4.55 20.70

3 41.95 45.89 3.94 15.52

2 42.31 45.48 3.17 10.04

1 43.05 45.10 2.05 4.20

Microscope readings and diameter of the rings

Figure- 6 Variation of Ring number with square of the diameter

d2

Slope = -------- = 0.054 cm2

n

Slope 0.054

Radius of curvature R = ---------- = ------------------- = 229 cm

4λ 4 x 5893 x 10-8

Results

Radius of curvature of the plano-convex lens = 229cms.

0

20

40

60

80

0 5 10 15

Ring Number (n)

Dia

met

er s

qu

are

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Discussions

1. Newton’s rings are observed and the radius of curvature of the lens is determined. As the value

of radius of curvature is fairly large, this method may be considered as an accurate method for

R measurements. It may be noted that, through a spherometer could be used to measure R, it

fails to give accurate results when the value of R is large.

Figure-6, Cross wire coinciding the rings

2. The accuracy of the measurement can be ascertained in the following way. The thickness of

the dark fringe forming the 1st ring is measured to be equal to 0.011mm. Error occurs

depending upon the displacement of the cross wire from the correct position. Maximum error

that can get in to the measurement will be half of the thickness i.e. 0.055mm. An inaccuracy of

0.055mm in the diameter value of 3.17mm results in an error of about ±1cm in the value radius

of curvature which is less than 0.5%

References

1. S P Basavaraju, A detailed textbook of Engineering Physics Practicals, Subhas Publications,

1999, Page- 19,35.

2. Khanna and Gulati, College Practical Physics, R. Chand & Co, 1999, Page- 218

Acknowledgements

The author acknowledges M/s Friends Scientific and Laboratory Instruments Company, Ambala

Cantt, manufacturer of Newton’s ring microscope, which is used in this experiment.

Cross wire reticuleof the microscopecoinciding left ofthe first ring