A PHYSICS PROJECT REPORT

Submitted by

ANUSHA PRASAD

In Partial Fulfillment Of The

CBSE GRADE XII

In

PHYSICS

AT

2013-2014

AECS MAGNOLIA MARUTI PUBLIC SCHOOL

#36/909, ARAKERE, BANNERGHATTA ROAD,

BANGALORE- 560076.

CERTIFICATE

This is to certify that ANUSHA PRASAD of Grade XII, AECS MAGNOLIA MAARUTI PUBLIC SCHOOL, BANGALORE with register number ____________________ has satisfactorily completed the project in Physics on TO MEASURE THE WAVELENGTH OF SODIUM LICHT USING NEWTON’S RINGS in partial fulfillment of the requirements of All India Secondary School Certificate Examination (AISSCE) as prescribed by CBSE in the year 2013-2014.

Signature of the Signature of the

Candidate Teacher In-Charge

Signature of the Signature of the

Principal External Examiner

Contents

1. ABBREVIATION...................................................................................................................1

2. INTRODUCTION...................................................................................................................2

3. THEORY................................................................................................................................4

4. SCOPE AND LIMITATION.................................................................................................10

5. APPARATUS........................................................................................................................12

6. DESCRIPTION OF COMPONENTS....................................................................................13

6.1 SODIUM LAMP.............................................................................................................136.2 TRAVELLING MICROSCOPE........................................................................................146.3 PLANO- CONVEX LENS...............................................................................................156.4 SPHEROMETER............................................................................................................16

7. PROCEDURE.......................................................................................................................18

8. OBSERVATION...................................................................................................................20

8.1 TABLE FOR DETERMINATION OF (D2N+P – D2N).......................................................208.2 TO DETERMINE RADIUS OF CURVATURE OF CONVEX LENS..................................21

9. CALCULATIONS.................................................................................................................22

9. 1 TO FIND THE DIAMETER OF NEWTON’S RINGS.....................................................................229.2 TO FIND THE RADIUS OF CURVATURE OF THE CONVEX LENS.................................................22

10. RESULT............................................................................................................................23

11. CONCLUSION..................................................................................................................24

12. BIBLIOGRAPHY.............................................................................................................25

ACKNOWLEDGEMENT

I would like to thank my teachers, Mrs. Bernali and Mrs. Jayathi for guiding me through this project and for their valuable inputs which provided me with a constant nudge for improvement.

It is imperative to thank our Principal, Mrs. Seema Goel for providing me the opportunity to work on this project.

It goes without saying that my classmates, especially Abhirami, Madhumati, and Shruthi for their help in due course of this project. My parents have also played a part in helping me in this project. My thanks goes out to them also.

This project and reading-up on the same has provided me with an in depth understanding of the topic. It has nurtured my scientific temperament and curiosity.

Signature of the

Candidate

1. ABBREVIATION

Sl.No Abbreviation Expansion

1 M.S.R Main Scale Reading

2 L.S.R Linear Scale reading

3 T.R Total Reading

4 C.S.R Circular Scale Reading

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2. INTRODUCTION

Newton’s rings, in optics, is a series of concentric light- and dark-coloured bands observed between two pieces of glass when one is convex and rests on its convex side on another piece having a flat surface. Thus, a layer of air exists between them. The phenomenon is caused by the interference of light waves—i.e., the superimposing of trains of waves so that when their crests coincide, the light brightens; but when trough and crest meet, the light is destroyed. Light waves reflected from both top and bottom surfaces of the air film between the two pieces of glass interfere.

The phenomenon was first described by Robert Hooke in his 1664 book Micrographia, although its name derives from the physicist Isaac Newton, who was the first to analyze it.

The principle is often used in testing the uniformity of a polished surface by studying the interference pattern the surface makes when placed in contact with a perfectly flat glass surface.

The outer rings are spaced more closely than the inner ones. Moving outwards from one dark ring to the next, for example, increases the path difference by the same amount, λ, corresponding to the same increase of thickness of the air layer, λ/2. Since the slope of the convex lens surface increases outwards, separation of the rings gets smaller for the outer rings. For surfaces that are not convex, the fringes will not be rings but will have other shapes.The phenomenon of Newton’s rings is used to calculate the wavelength of monochromatic

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A thin wedge shaped air film is created by placing a plano-convex lens on a flat glass plate. A monochromatic beam of light is made to fall at almost normal incidence on the arrangement. Ring like interference fringes are observed in the reflected light. The diameters of the rings are measured.

Newton’s rings" interference pattern created by a plano-convex lens illuminated by 650nm red laser light, photographed using a low-power microscope.

How the interference fringes form.

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3. THEORY

Thin film interference with films of varying thickness (Newton’s rings):

Rings are fringes of equal thickness.  They are observed when light is reflected from a plano-convex lens of a long focal length placed in contact with a plane glass plate.  A thin air film is formed between the plate and the lens. 

The thickness of the air film varies from zero at the point of contact to some value t.  If the lens plate system is illuminated with monochromatic light falling on it normally, concentric bright and dark interference rings are observed in reflected light. 

These circular fringes were discovered by Newton and are called Newton’s rings. A ray AB incident normally on the system gets partially reflected at the bottom curved surface of the lens (Ray 1) and part of the transmitted ray is partially reflected (Ray 2) from the top surface of the plane glass plate.   The rays 1 and 2 are derived from the same incident ray by division of amplitude and therefore are coherent.  Ray 2 undergoes a phase change of p upon reflection since it is reflected from air-to-glass boundary.

The condition for constructive and destructive interferences are given as; for normal incidence  cos r = 1 and for air film     = 1.

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………………..(Constructive interference)

   ……… ………..(Destructive interference)

 

1. Central dark spot: At the point of contact of the lens with the glass plate the thickness of the air film is very small compared to the wavelength of light therefore the path difference introduced between the interfering waves is zero. Consequently, the interfering waves at the centre are opposite in phase and interfere destructively. Thus a dark spot is produced.

2. Circular fringes with equal thickness: Each maximum or minimum is a locus of constant film thickness. Since the locus of points having the same thickness fall on a circle having its centre at the point of contact, the fringes are circular.

3. Fringes are localized: Though the system is illuminated with a parallel beam of light, the reflected rays are not parallel. They interfere nearer to the top surface of the air film and appear to diverge from there when viewed from the top. The fringes are seen near the upper surface of the film and hence are said to be localized in the film.

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4.  Radii of the mth dark rings……… 

5. Radii of the mth bright ring………

The radius of a dark ring is proportional to the radius of curvature of the lens by the relation,   . Rings get closer as the order increases (m increases) since the diameter does not increase in the same proportion.

In transmitted light the ring system is exactly complementary to the reflected ring system so that the centre spot is bright. Under white light we get colored fringes

The wavelength of monochromatic light can be determined as………………..    

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Where, Dm+p  is the diameter of the (m+p)th dark ring andDm is the diameter of the mth dark ring. 

This method for determining the wavelength of light was proposed by Sir Isaac Newton in his book Opticks, published in 1717. The experimental arrangement is shown in Figure 1.

A plano-convex lens of large radius of curvature R is placed on a plane glass plate with its curved surface downwards and is illuminated from above with a parallel beam of monochromatic light. Some of the light is reflected from the upper surface of the glass plate and some from the lower surface of the lens; interference thus occurs by division of amplitude, the fringes being localised in the air gap between the lens and plate.

At any point a distance r from the axis of the lens the path difference will be2h, where h is the distance between the lens and the plate at that point (SeeFigure 2). The interference fringes are circular because the system is symmetrical about the centre of the lens. The radius of any ring is given by:

(2R – h)h = r2  so r2 = 2 Rh - h2

But h2 is small compared with 2Rh and so we can write: 2Rh = r2

The path difference (2h) is therefore r2/R 

A phase change of p occurs when the light reflects from the top surface of the plate but not at the lower surface of the lens, and therefore:

For a bright ring viewed by reflection:   (2m + 1)λ/2 = rm2/R

For a dark ring viewed by reflection:      mλ = rm2/R

Where m = 0, 1, 2, 3, etc and rm is the radius of the mth ring.

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If a graph is plotted of r2 against m for the dark rings a straight line should be produced with a gradient given by:

(rm2 - r1

2)/(m - 1) = lR

where r1 and rm are the radii of the first and mth rings respectively. (See Figure 3).

When doing the experiment it is much easier (and more accurate) to measure the diameter of the rings and then calculate their radius. A dark central spot should be obtained when viewed by reflection. 

The rings can be viewed by transmission by putting the microscope below the plate, and if this is done the equations for bright and dark rings should be

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interchanged as two phase changes will occur, producing an effective path difference of 2p. A bright central spot should be obtained.

If white light is used a few coloured rings will be seen due to the different wavelengths of the different colours of light.

Newton's rings and the refractive index of a liquid

Putting a liquid of refractive index n between the lens and the plate (Figure 5) will change the path difference to 2nh and give a formula for the m th dark ring of: 

mλ = [nrm2]/R

6. The radius of any given ring will be less with the liquid in place than without it. This effect may be used to measure the refractive index of the liquid; the method is a good one since it is accurate and easy to perform, and only a small amount of the liquid is needed.

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4. SCOPE AND LIMITATION

The interference technique of Newton’s Rings is widely used for the quality

control of optical surfaces because the precision obtained with this method

proves to be very satisfactory. The dimensions of the rings permits

calculation of the radii of curvature of the analysed surfaces and deformation

of the interference pattern can be utilised to calculate other parameters, such

as astigmatism. We describe the study of progressive surfaces by means of

this technique, whereby the analysis of the various points of the progressive

corridor is made, and also include information on the power function for

these lenses, as well as the addition and corridor length.

They can be used to get a measure of how flat surfaces are. A very flat sheet

of glass, lying on top of the surface of interest will show puddles of

Newton’s rings around depressions and raised areas - best to use

monochromatic light to view them with. Counting the rings and knowing the

wavelength of the illumination can give an accurate measure of the size of

any hollows and heights on a surface.

However, there are few important precautions which must be taken in order

to successfully complete this experiment. They are as follows:

The thin film must be inserted carefully between the plain glass plate and plano convex lens without disturbing the fringes. 

NB A high-pressure sodium street lamp as used in colour studies will not give sharp fringes in this experiment. If the centre fringe is not dark, try polishing the lens and flat with a spectacle cleaning cloth.

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Sodium metal is very reactive when it is exposed to air. Hence sodium light is covered with strong silicate glass. Thus proper care must be taken while handling with the sodium lamp. It should be ensured that the glass doesn’t get damaged.

There might be errors in the travelling microscope or the spherometer which will result in erroneous values. Hence zero errors must also should be taken into account.

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5. APPARATUS

Requirements:

a. Apparatus Requirement

Sodium vapour lamp Travelling Microscope Spherometer Plano Conves lens Glass plate Focussing lens Power supply with cord.

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6. DESCRIPTION OF COMPONENTS

6.1 SODIUM LAMPA sodium-vapor lamp is a gas-discharge lamp that uses sodium in an excited state to produce light. There are two types of sodium lamps: the low pressure sodium lamp (LPS) and the high pressure sodium lamp (HPS). A low pressure sodium lamp is used in this experiment as high pressure sodium lamps will not give sharp fringes in this experiment.

Low-pressure sodium (LPS) lamps have a borosilicate glass gas discharge tube (arc tube) containing solid sodium, a small amount of neon, and argon gas in a Penning mixture to start the gas discharge.

When the lamp is turned on it emits a dim red/pink light to warm the sodium metal and within a few minutes it turns into bright yellow as the sodium metal vaporises. These lamps produce a monochromatic light averaging a wavelength of 589.3 nm. LPS lamps have an outer glass vacuum envelope around the inner discharge tube for thermal insulation, which improves their efficiency.

It is among the most efficient lamps in the world because it uses all the current it gets to create light at the most sensitive frequency to the human eye.

The advantages of sodium lamps are:

Very efficient lamp Despite a warm up time of 5-10 minutes it restarts immediately if there is

a brownout Lumen output does not drop with age

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An LPS with its yellow glow

6.2 TRAVELLING MICROSCOPE

Travelling Microscope

A travelling microscope is an instrument for measuring length with a resolution typically in the order of 0.01mm. The precision is such that better-quality instruments have measuring scales made from Invar to avoid errors due to thermal effects. The instrument comprises a microscope mounted on two rails fixed to, or part of a very rigid bed. The position of the microscope can be varied coarsely by sliding along the rails, or finely by turning a

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screw. The eyepiece is fitted with fine cross-hairs to fix a precise position, which is then read off the vernier scale.

Travelling microscope consists of a cast iron base with machined-Vee-top surface and is fitted with three leveling screws. A metallic carriage, clamped to a spring-loaded bar slides with its attached vernier and reading lens along an inlaid strip of metal scale. The scale is divided in half millimeters. Fine adjustments are made by means of a micrometer screw for taking accurate reading. Both vernier reading to 0.01mm or 0.02mm. Microscope tube consists of 10x Eyepiece and 15mm or 50mm or 75mm objectives. The Microscope, with its rack and pinion attachment is mounted on a vertical slide, which too, runs with an attached vernier along the vertical scale. The microscope is free to rotate n vertical plane. The vertical guide bar is coupled to the horizontal carriage of the microscope. For holding objects a horizontal stage made of a milky conolite sheet is provided in the base.

6.3 PLANO- CONVEX LENS

Plano Convex Lens

A lens which has one side plane and the other side convex, is called a plano convex lens.

Plano-convex lenses are used to collimate diverging light or to focus collimated light. They are used as secondary focusing lenses to refocus the collimated light sources. Plano-convex lenses have low spherical aberration.

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This is the most common type of lens element.  It is also useful as a simple imaging lens where image quality requirement is not too critical.

6.4 SPHEROMETER

Spherometer

A spherometer is used to measure either very small thickness or the radius of curvature of a spherical surface. It works on the principle of micrometer screw.

The spherometer consists of a metallic tripod framework supported on three fixed legs of equal lengths. The tips of the three legs lie on the corners of an equilateral triangle and always lie on the same plane. At the centre of the tripod frame is fixed a vertical nut through which passes, an accurately cut screw. A large circular disc terminating into a milled head is attached at the top of the screw. The circumference of the circular disc is divided into 100 or 200 equal parts. A small vertical scale is fixed at one end of the tripod stand, parallel to the axis of the screw and just touching the rim of the circular disc.

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The least count of a spherometer is usually 0.001cm. The least count is calculated using the formula, L.C.=p/N where p is the pitch and N is the number of divisions on the circular scale.

In this experiment, the spherometer is used to calculate the radius of curvature of the plano convex lens.

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7. PROCEDURE

If a point source is used only then we require a convex lens otherwise while using an extended source, convex lens L1 is not required.

1. Before starting the experiment, the glass plates & the Plano convex should be thoroughly cleaned.

2. The center of lens is well illuminated by adjusting the inclination of glass plate at 45 deg.

3. Focus the eyepiece on the crosswire and move the microscope in the vertical plane by means of rack & pinion arrangement till the rings are quite distinct clamp the microscope in the vertical scale.

4. According to the theory, the center of the interference fringes should be dark but sometimes the center appears white, this is due to the presence of dust particles between glass plate and Plano convex lens. In this case lens should be again clean.

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5. Adjustments should be done till satisfactory fringe system of perfect circular shape with a dark spot at the centre is obtained.

6. First, the microscope is adjusted so that the centre of the cross wires coincides with the central dark spot of the fringe system. The microscope is then moved slowly either towards left or right of the centre.

7. While the microscope is moved, the number of dark rings is counted say, up to 14.At the 14th dark ring the microscope is stopped and its motion is reversed. It is brought back to the position of 12th ring. The vertical cross wire is adjusted such that it will be tangential to the 12th dark ring. In this position the reading of the microscope is noted.

8. The microscope is then moved to the 10th dark ring such that the vertical cross wire is again tangential to the ring. The reading of the microscope is noted. The above process is continued till 2th dark ring is reached.

9. After taking the reading for the 2th ring the microscope is moved in the same direction on to the opposite side of the centre. The microscope is moved till the 2th dark ring on the opposite side is reached. The reading is taken as before for the 2th dark ring.

10.The measurements are continued on the opposite side till 12th dark ring is reached.

11.The observations are noted in table.

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8. OBSERVATION

Value of one division of the main scale = 0.001 cm

No of division on the vernier scale = 50

Least count of the travelling microscope = 0.001 cm

8.1 TABLE FOR DETERMINATION OF (D2n+p – D2n)

Sl.No.

OrderLHS Reading(in cm)

RHS reading(in cm)

DiameterD =(L~R)

D2

(in cm2)D2

n+p – D2n

(in cm2)D2

n+p – D2n/ 4mR

(in cm2)

MSR VSR TR(L) MSR VSR T.R

1. 10 2.4 35 2.435 2 20 2.02 0.414 0.17222 0.01856 5948

2. 9 2.4 2 2.402 2 10 2.01 0.392 0.15366 0.01824 5846

3. 8 2.25 16 2.266 1.85 48 1.898 0.368 0.13542 0.01914 6134

4. 7 2.2 36 2.236 1.85 45 1.895 0.341 0.11628 0.01831 5868

5. 6 2.15 48 2.198 1.85 35 1.885 0.313 0.09797 0.03547 -

6. 5 2.1 25 2.125 1.85 25 1.875 0.213 0.0625 0.01746 5628

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Sl.No.

OrderLHS Reading(in cm)

RHS reading(in cm)

DiameterD =(L~R)

D2

(in cm2)D2

n+p – D2n

(in cm2)D2

n+p – D2n/ 4mR

(in cm2)

MSR VSR TR(L) MSR VSR T.R

7. 4 2.05 27 2.077 1.85 15 1.865 0.212 0.04494 0.01771 5676

8. 3 2 10 2.01 1.8 45 1.845 0.165 0.02723 0.01913 6131

9. 2 1.9 5 1.905 1.8 15 1.815 0.09 0.0081 - -

8.2 TO DETERMINE RADIUS OF CURVATURE OF CONVEX LENS

Value of one linear scale division = 1mm

Linear distance moved = 1mm

No. of rotations given = 1

Pitch = 1mm

Least count = pitch/ no. of divisions on circular scale

No. of divisions on circular scale = 100

Least count = 0.01mm

C.S.R. on convex surface (in mm)

A

C.S.R on plane surface (in mm)

B

CompleteRotations - n

IncompleteRotationsx = A-B

H = n*p + x*L.C (in mm)

39 20 0 19 0.19

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9. CALCULATIONS

9. 1 To find the diameter of Newton’s ringsMean wavelength of sodium light = 5890 A

9.2 To find the radius of curvature of the convex lens Length of the sides:

L1 = 2.98 cm

L2 = 3 cm

L3 = 2.96 cm

Mean = 2.98 cm

H = 0.019 cm

R= (L2 /6H) + (H / 2)

= 78 cm

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10. RESULT

The mean wavelength λ of sodium light = 5890 Å

Standard mean wavelength λ = 5890 Å

Percentage Error = 0%

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11. CONCLUSION

The standard wavelength and the experimental wavelength were both found to be λ = 5890 Å with no error percentage existing.

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12. BIBLIOGRAPHY

http://www.edisontechcenter.org/SodiumLamps.html http://en.wikipedia.org/wiki/Sodium-vapor_lamp www.google.com www.vedupro.blogspot.in http://www.nuffieldfoundation.org/practical-physics/application-

newtons-rings-experiment NCERT physics text book part 2 class XII Comprehensive lab manual class XII

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