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Interference by multiple beam reflections: Newton’s RingsAim: 1. Studying the interference phenomenon due to multiple reflections of light waves from gradually varying air film. 2. Determination of the wavelength of a monochromatic light using Newton’s rings.Apparatus: Plano – convex or bi - convex lens, monochromatic light (sodium or laser light), traveling microscope, spherometer. Theory When a plano-convex lens with its convex surface is placed on a plane glass sheet, an air film of gradually increasing thickness outward is formed between the lens and the sheet. The thickness of film at the point of contact is zero. If monochromatic light is allowed to fall normally on the lens, and the film is viewed in reflected light, alternate bright anddark concentric rings are seen around the point of contact. These rings were firstdiscovered by Newton, thats why they are called NEWTONS RINGS.When monochromatic light is incident on a thin film of refractive index nconfined between two dielectric surfaces (glass, for instance), then part of thelight will be reflected at the upper surface and part of it will be refracted to thelower glass surface where it undergoes multiple reflections before being able totransmit back to the upper surface as illustrated in figure 1. Thus, at the uppersurface there will be two kinds of waves: I. Waves that reflect directly at the upper optically denser medium to a lower optical density medium (light ray 1). Here, the reflected wave undergoes a phase change of 180o on reflection. II. In this kind, the waves undergo either one internal reflection (light ray 2) or many of this reflections Light Beam Reflected light Beam (light rays 3,4,5,…) prior no 1 2 3 4 5 to being refracted to the lesser optical density medium. nIf the film thickness is d and ofrefractive index n, and thelight is allowed to incidentnormally to the film, the Figure 1 Transmitted Light Beam Newton’s Rings page 1 of 7 Tuesday, May 22, 2012 Baghdad University – College of Science – Department of Physics – Optics Laboratory Administration Tele: +009647702981421
Interference by multiple beam reflections: Newton’s Ringsoptical path difference between any two rays is given by:Rays 1, 2, 3, 4, … may interfere and interference fringes will be viewable if thereflected rays are converged by a convex lens.Newton discovered that interference fringes may also be generated by an air filmof varying thickness (i.e., the two surfaces confining the air film are not parallel).For an air film of varying thickness to be formed, a convex or Plano – convex lensis laid over a plane glass plate G, figure 2. Using a thin glass sheet inclined at 450angle with respect to the incident light beam, i.e., with the horizon, part of the rm R R 1 2 M R-dm L L rm do dm do+ d G G T T Figure 2: creating Newton’s Ringslight will be reflected towards the air film. When a light ray is incident on theupper surface of the lens, it is reflected as well as refracted. When the refractedray strikes the glass sheet, it undergoes a phase change of 180O on reflection.When looking to the light rays reflected from both the lens L and the glass plate Gthrough the eyepiece of a traveling microscope focused at the glass plate G,successive dark and bright concentric circular fringes “Newton’s rings” occurthrough monochromatic light interfering in the thin intermediate film between aconvex lens and a plane glass plate. Ray 1 reflected at the underside of the lensthus interferes with ray 2 reflected at the top of the glass plate.The film of air at a distance r from the point of contact between the lens and theglass plate has a thickness D = d ± do. As ideal contact is not present, we must takedo into account. do is positive when, for example, there are particles of dustbetween the lens and the glass plate, but is can so also be negative when thepressure is greater. In either case, the central may be bright or dark of unknown Newton’s Rings page 2 of 7 Tuesday, May 22, 2012 Baghdad University – College of Science – Department of Physics – Optics Laboratory Administration Tele: +009647702981421
Interference by multiple beam reflections: Newton’s Ringsorder of interference. On the other hand, if the pole of the lens is in intimatecontact with the glass block, then the central fringe will be dark of order ofinterference m=0. The geometrical path difference of the interfering rays istherefore:In addition, the ray reflected from the plane glass surface experiences a phaseshift always occurs when light travels from the optically thinner towards theoptically denser dielectric medium and is partially or totally reflected at theinterface. The effect of this corresponds to a distance travelled of length . Inall, therefore, there is an apparent path difference, therefore:The optical path difference between the two – type reflections:For the interference rings of maximum cancellation, i.e. dark fringes, the opticalpath difference equals even multiple of , thus:OrIn accordance with Figure 2, and using simple trigonometry, a relation betweenthe radius rm of the mth dark ring, the thickness d and the radius of curvature R ofthe plano-convex lens (in the ideal case do = 0) may be derived. Thus:In case of slightly convex lenses, , so that may be neglected and theprevious equation becomes: Newton’s Rings page 3 of 7 Tuesday, May 22, 2012 Baghdad University – College of Science – Department of Physics – Optics Laboratory Administration Tele: +009647702981421
Interference by multiple beam reflections: Newton’s RingsThus, the thin film thickness dm may be given in term of the mth ring radius rm (ordiameter Dm) as follows:Therefore, the conditions for the dark and bright interference fringes will be:Like the Haidinger fringes, Newton’s rings are also circular, but the two differ atthe fundamental level. The center of the Haidinger fringe pattern is occupied bythe fringe of the highest order which may be bright, dark, or may have anyintermediate intensity. The center of the Newton’s ring pattern in reflected lightalways has a dark fringe of the lowest order. It is somewhat puzzling why thesefringes are named after Newton since Newton was not a believer of the wavetheory of light.For the evaluation, is plotted against m. The wavelength of the transmittedlight is obtained from the slope of the straight line:In the set-up Figure 3: Radius of the interferencedescribed, the rings as a function of theNewton’s rings are order number.observed intransmitted light.The interferencerings arecomplementary tothose in reflectedlight. In the latter 0 mcase, therefore, thelight rings are counted and not the dark ones.Procedure Newton’s Rings page 4 of 7 Tuesday, May 22, 2012 Baghdad University – College of Science – Department of Physics – Optics Laboratory Administration Tele: +009647702981421
Interference by multiple beam reflections: Newton’s Rings 1. The experiment is set up by putting the plano – convex lens over the glass plate. Both the lens L and the glass plate G should be thoroughly clean and dust – free. 2. The traveling microscope is focused on the glass plate. To achieve this, a paper with a mark may be placed over the glass plate and the traveling microscope is moved up and down till getting a sharp and distinct image of the mark in the eyepiece field of view. 3. The 450 angled beam splitter glass plate is illuminated with a monochromatic light (sodium light or any other coherent light). 4. Doing so, Newton’s rings should now be viewable at the focal plane of the traveling microscope’s eyepiece. The ring pattern may not be extremely sharp and, thus, blurred. This problem can be easily overcome by adjusting focusing the traveling microscope eyepiece relative to the plano – convex lens since it was focused on the glass plate. 5. Before measurements are to be taken, its important to insure that the central spot is dark and not bright!! Why? 6. Measurement of the radius (or diameter) of a suitable set of successive rings is to be done by recording the vernier reading after making the eyepiece’s cross hairs at the right and left sides of each dark interference ring. Its advisable to start taking the measurements from the left – hand side of say, the 5th dark ring, and keep moving the traveling microscope in the same direction, i.e. to the right – hand side. This is essential to avoid the backlash error. 7. The radius of curvature of the plano – convex lens can be calculated by the spherometer. 8. A graph of is plotted against m. The wavelength , in nm, of the transmitted light is obtained from the slope of the straight line. Microscope’s Venire Microscope’s Venier Ring Radius Ring Order mth Ring Radius Reading Reading Squared m rm cm XR cm XL cm r2m cm2 5 4 3 2 1Discussion Newton’s Rings page 5 of 7 Tuesday, May 22, 2012 Baghdad University – College of Science – Department of Physics – Optics Laboratory Administration Tele: +009647702981421
Interference by multiple beam reflections: Newton’s Rings 1. What are the coherent sources generating the ring interference pattern? How about their types (real, virtual, one real and the other virtual)? 2. Is the pattern central spot dark or bright? Why? Write down its equation giving explanation to your choice of the equation. 3. If the interference rings were not circular in shape and deformed, what would the reason for this be? How can it be fixed? 4. Why are the interference fringes circular instead of being straight? Confirming the answer with mathematical equation will be credited. 5. Show with schematic diagram how the current experiment can be modified to measure the refractive index of a fluid (liquid or gas). How will the final formula look like? 6. Does the interference pattern change upon using a lens of higher radius of curvature? Illustrate how the diameters of the interference rings will be affected. Confirming the answer with mathematical equation will always be credited. 7. Newton’s rings are observed with a 10 m radius of curvature plano-convex lens resting on a plane glass plate. (a) Find the radii of the dark interference rings of the various orders observed by reflection under nearly perpendicular incidence, using light of wavelength 4.8 10-7 m. (b) how many rings are seen if the diameter of the lens is 4 cm? 8. Why is it so much easier to perform interference experiments with a laser than with an ordinary light source? 9. A lens with outer radius of curvature R and index of refraction n rests on a flat glass plate. The combination is illuminated with white light from above and observed from above. Is there a dark spot or a light spot at the center of the lens? What does it mean if the observed rings are noncircular? 10. A plano-concave lens having index of refraction 1.50 is placed on a flat glass plate. Its curved surface, with radius of curvature 8.00 m, is on the bottom. The lens is illuminated from above with yellow sodium light of wavelength 589 nm, and a series of concentric bright and dark rings is observed by reflection. The interference pattern has a dark spot at the center, surrounded by 50 dark rings, of which the largest is at the outer edge of the lens. (a) What is the thickness of the air layer at the center of the interference pattern? (b) Calculate the radius of the outermost dark ring. (c) Find the focal length of the lens. 11. In a Newton’s-rings experiment, a plano-convex glass (n = 1.52) lens having diameter 10.0 cm is placed on a flat plate. When 650-nm light is incident normally, 55 bright rings are observed with the last one right on the edge ofNewton’s Rings page 6 of 7 Tuesday, May 22, 2012 Baghdad University – College of Science – Department of Physics – Optics Laboratory Administration Tele: +009647702981421
Interference by multiple beam reflections: Newton’s Rings the lens. (a) What is the radius of curvature of the convex surface of the lens? (b) What is the focal length of the lens? 12. Are Newton’s rings obtainable with the transmitted light beam of figure 1? 13. Why does not the straight line in figure 3 pass through the origin? 14. When is the presence of the 450 angled beam splitter glass plate not necessary? 15. A plano-convex lens having a radius of curvature of R = 4.00m is placed on a concave glass surface whose radius of curvature is R =12.0 m. Determine the radius of the 100th bright ring, assuming 500-nm light is incident normal to the flat surface of the lens. 16. Does a phase shift of π occur when light travels from the optically thinner towards the optically denser metallic medium? 17. What is meant by “fringe of equal inclination”, “fringe of equal thickness”? 18. In the current experiment, does light behave like a particle (photons) or like a wave or both?Newton’s Rings page 7 of 7 Tuesday, May 22, 2012 Baghdad University – College of Science – Department of Physics – Optics Laboratory Administration Tele: +009647702981421