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Determination of the width of a paper employing wedge interference phenomenonAim: evaluating the width of a sheet of paper via wedge interference phenomenon.Apparatus: microscope glass slide, thick glass plate (opaque one is preferable), traveling microscope, convex lens. Theory When a piece of paper of width t is introduced between the edges of two transparent glass plates, a thin wedge – shape air film will be formed as illustrated in figure 1. The monochromatic light incident normally on the air wedge will be divided into two parts by the wave amplitude – division method. One part is reflected at the upper glass surface OP andthe other part passes to the lower glass surface OP’ where it undergoes a furtherreflection upon striking that surface. Since this reflection is from an opticallydenser (higherrefractive index) Travelingmedium (glass) to Microscopea lower optical Convexdensity medium Lens(air), the reflectedlight waves will be 45phase shifted by180o (this is Glassequivalent to an plate Coherentadditional optical Light Beampath difference of P B Sheet between the Of ttwo upper and A C Paper αlower reflected O A B’ P’ ’beams). Due to the yoverlapping ℓ(interference) of Figure 1: experimental set – up of air –the two reflected wedge interference phenomenonlight beams, brightand dark straightfringes are observed in the traveling microscope’s field of view. Wedge interference phenomenon page 1 of 4 Tuesday, May 22, 2012 Baghdad University – College of Science – Department of Physics – Optics Laboratory Administration Tele: +009647702981421
The fringe at point A is formed by interfering light ray, reflected off the upperglass surface OP, with the one reflected from the lower glass plate which suffereda 180o - phase shift in addition to traversing double the distance AA’ when itpropagates back and forth. If the total phase shift equals odd multiples of half thelight wavelength, then a dark interference fringe will be formed. On the otherhand, the interference fringe will be bright whenever the total phase shift equalseven multiples of the light wavelength used. The next interference fringe formedat point B is due to the increase of air – wedge width by an amount of half thelight wavelength (the distance BC in the figure 1).If α is the wedge angle in degrees, then from the triangle ABC it is apparently that:Where: y represents the distance between two successive (dark or bright)fringes. In the triangle OPP’:Where t=PP’ represents the width of the paper in mm unit and is theseparation between the inner edge of the paper and line of contact of the twoglass plates.Procedure: 1. A convex lens is used to get a parallel light beam emerging from the monochromatic light source (typically the monochromatic sodium light or any other coherent light source, for example He-Ne laser light ). This parallel light beam is to be making - angle of incidence with a horizontally oriented, - angle, half – silvered glass plate. The light rays reflected off this plate will perpendicularly incident on the lower thick glass plate of the air – wedge. 2. The traveling microscope is then focused until getting the lower thick glass plate of the air – wedge at the focal plane of the traveling microscope’s eyepiece. Doing so, a distinct interference pattern should become viewable. 3. The distance between a suitable number of dark (or bright) fringes is measured using the traveling microscope vernier and the width of the dark of bright fringe is deduced by dividing the measured distance on the number of fringes. The measurement is then recorded in a suitable table. Wedge interference phenomenon page 2 of 4 Tuesday, May 22, 2012 Baghdad University – College of Science – Department of Physics – Optics Laboratory Administration Tele: +009647702981421
4. Step 3 is repeated for a number of times and the average of such measurements is evaluated. 5. Using a micrometer vernier, the distance is measured. 6. Finally, the width of the paper t is estimated by applying formula 1.Discussion: 1. How is light behaved in this experiment? 2. What is the appearance of interference fringes formed in the air – wedge? Why do they appear like this? Stating the mathematical equation is preferable. 3. What is the type of interference fringe (i.e., dark or bright) formed at the contact line of the two glass plates? How about its equation? Explain your answer. 4. Does wedge interference phenomenon depend on wave front division or wave amplitude beam splitting? State other experiments which depend on the same operating principle. 5. Evaluate the optical path difference of the sixth dark fringe assuming that the medium between the two glass plates is air once and water in the other and the light source used is the sodium monochromatic light. 6. How can the air – wedge experiment be modified to measure the refractive index of unknown liquid, for example water? How will the final formula look like? Can you derive this formula? No doubt, you can!! 7. Point out natural daily phenomena in which multiple – reflection interference is truly confirmed. 8. If sodium monochromatic light is replaced by polychromatic light (white light for instance), will the interference pattern remain viewable? How will the fringes look like? Why? Wedge interference phenomenon page 3 of 4 Tuesday, May 22, 2012 Baghdad University – College of Science – Department of Physics – Optics Laboratory Administration Tele: +009647702981421
“A candle loses nothing of its light in lighting another”. J. K. Jibran Wedge interference phenomenon page 4 of 4 Tuesday, May 22, 2012Baghdad University – College of Science – Department of Physics – Optics Laboratory Administration Tele: +009647702981421