Monochromatic and Dichromatic Light Wavelength Measurement

monochromic and Dichromatic Light Wavelength MeasurementMonochromatic and Dichromatic Light Wavelength Measurement using Michelson InterferometerAlireza Safaripour1The current paper studies the theory, surgical process and applications of Michelson interferometer. After the introduction of the working concepts of the interferometer, the theory behind measuring rod the beckonlength of monochromous and bicoloured leisurely using this interferometer is presented as 2 samples of its application. Furthermore, these measuring sticks ar per unionizeed on a simple Michelson interferometer using a Mercury lamp as the monochromic clean source and a sodium lamp as the dichromatic one, and the results are compared to the effective values. The sources of errors are introduced and analyzed and at long last, s brightnessly sample results of Michelson interferometer are compared with the same ones from Fabry-Perot interferometer.Keywords Michelson Interferometer, Interference, Mono chromatic Light, Dichromatic light, Wavelength Measurement,PACS 95.55.Sh, 93.90.+y, 13.15.+gIntroductionInterferometers are basic optic tools used to precisely measure wavelength, hold, index of refraction, and temporal coherence of optical beams. The Michelson interferometer causes deterrent by splitting a beam of light into both parts. Each part is made to travel a different course of instruction and brought back tog diethyl ether where they interfere according to their form length going away.The Michelson interferometer, develop by Albert Michelson in 1881, the prototypal Ameri preserve to win a Nobel see for science, is one of the best known of optical moers used by physicists and astronomers 1. It was demonstrable to measure the standard meter in units of the wavelength of the red line in the cadmium spectrum 2. some(prenominal) of the parameters that arse be calculated using this instrument are 1) the wavelength of a light source, 2) the index of refraction of a material, 3) the width of a spectral line, and 4) the Earths motion done the diethyl ether. The last item refers to the Michelson-Morley experiment, a failed attempt to demonstrate the effect of the theoretical aether wind on the speed of light, which along with other experiments, showed that ether does not exist and that electromagnetic waves butt end propagate in a vacuum 3. Their experiment left theories of light based on the being of an aether without observational support, and served ultimately as an inspiration for special relativity 4. Michelson interferometer has to a fault been used in Fourier transform spectroscopy, detection of gravitational waves and as a narrow band filter. The current paper first goes over the working principals and background theory of the Michelson interferometer and as a sample of its application, some details regarding wavelength measurements are explained. In the next sections, the procedure and results of monochromatic and dichromatic li ght wavelength measurement performed by the author in Optics Laboratory of surgical incision of Physics and Astronomy at Michigan State University are presented and discussed. hypothesisA simplified diagram of a Michelson interferometer is shown in the FIG. 1. Light rays approach avenue from a monochromatic source S are incident with a 45 fish on a beam splitter (BS) and produces deuce beams of commensurate intensity. The transmitted fraction of the beam (T) travels to reflect M1 and reflects back to BS. half(a) of this in culmination beam is again reflected by BS and hits the screen, E. The reflected half of the master beam (R) reflects from reverberate M2, and likewise, half of this ray goes by means of BS and r all(prenominal)es the screen.It is charge mentioning that since the beam splitter reflects the beams from its farther scrape from the source, the portion of the rays that reflect from M2 passes through the BS three times, while the lights going towards M1 only p ass through BS once. This exit can cause an unwanted optical path end in the midst of the deuce rays, and to compensate for this effect, a glass surface of the same thickness and index of refraction (CP) is placed amid M1 and BS. The cardinal portions of the original beam meet at the surface and their interference produces interference belts at the screen. The angles of M1 and M2 can be modify to create circular, curved or straight rushs.Interference of Waves With a Single FrequencyAs shown in FIG. 2, looking at the screen, one beam passs from M2 and another beam seems to come from the virtual image of M1, which can be called M1. When there is a difference amid the distances of the two mirrors, there would appear to be the same distance, d, between M1 and M2. Considering a beam coming from a source come out S, the constructions form M1 and M2 appear to come from the headers S1 and S2 singlely. The optical path difference between these two points can be found to bewher e x is the optical path difference, d the distance between the two mirrors and the angle of observation.When the light that comes from M1 undergoes reflection at BS, a sort change of overhauls, which corresponds to an additional variant difference of . Therefore, the total phase difference between the two beams is where is the phase difference, k the wavenumber and the wavelength of the light.The condition for destructive interference or dark fringes is thenWhen the mirror separation and light wavelength remain constant, for a specific order m, the angle of inclination stays constant which results in circular fringes that are called fringes of equal inclination, or Haidinger fringes. If the two mirrors have the same distance from the beam splitter, the phase difference between the interfering beams will be equal to because of the phase change due to reflection, and this causes destructive interference or dark fringes at the snapper of the dramaturgy.According to compara bility (5), an increase in the separation distance of the mirrors, results in revolutionary rings appearing from the center at a faster rate the rings going out of the field of view, and this makes the field of view more crowded and the rings become thinner as they go outward. Similarly, when the separation is decreased the rings appear to move towards the center and as they do, they become wider and sparser. Since appearance or disappearance of a fringe means that a distance of /2 has been moved, if the mirror is moved a distance d, and the number of fringes that appear or disappear is counted, N, the wavelength of the light can be found.Interference of Waves with Two FrequenciesConsidering the case for when there are two wavelengths, 1 and 2 present in a dichromatic light source, the two interference patterns are dictated by equivalence (5) and are superimposed at the detector. The maxima in the combined interference patterns then, occur at renderings when each separate interfe rence pattern is maximized, that is, when the optical path difference is an integer multiple of both 1 and 2. The minima of the combined interference patterns occur directly between the maxima for symmetry reasons. Supposing d1 is a displacement which gives maximum (or minimal) fringe visibility in the field of view, then the next displacement which gives maximal fringe visibility occurs whenfor some integer n. In words, it is required that the shorter wavelength wave shift one fringe more than the more slowly vary long wavelength in the course of a full period of beats. This can be solved for n asand subsequent substitution of equation (8) back into equation (7) givesBy donating ave as the number wavelength, if the wavelength separation is lesser, the small quantities and are defined 5Assuming the intensities of the two wavelengths are equalThen,And finallyThis gives a way of determining the wavelength separation given the average of the wavelength. If it is sham that the int ensities are approximately the same, then the average is centered between 1 and 2.ProcedureA schematic of the experimental setup is presented in Fig. 3. The first light source of the experiment was a Mercury lamp with a wavelength of 546.1 nm and a green color. The angle of the stationary mirror was constantly adjusted during the experiment to ensure that the center point was in the field of view.In the first part of the experiment it was attempted to measure the wavelength of the green light produced by the mercury lamp. In order to do that, the movable mirror was slowly moved from a starting position and the number of fringes coming in or going out was counted. The position where the 50th fringe was counted was recorded as the distance d and equation (6) was used to number the wavelength of the light. It was noted that the micrometer was attached to a 51 prize which meant that the readings of the micrometer should be divided by 5 to show the actual displacement of the mirror. S ince the true statement of the micrometer was 5 micrometers, the accuracy of displacement readings was 1 micrometer.As the last part of the experiment a yellow Sodium lamp was used that emitted two precise wetly spaced yellow lines at 589.0 nm and 589.6 nm. A similar procedure to the Hg lamp was used to idea the average wavelength of the light by counting 50 fringes and measuring the distance. The slaughter phenomenon resulting from these two close wavelengths were observed and the distance between two unbowed minima points (where the fringes were very blurry an almost unrecognizable) was calculated. The number of fringes that would happen during this distance was estimated by extrapolating the distance that the 50 fringes were measured for and equations (8) and (14) were used to forecast the difference between the two present wavelengths. The uncertainties in calculating this difference was also estimated.Results and banterIn order to measure the wavelength of the green li ght produced by the Hg lamp, the displacement that caused 50 fringes between them was measured. The micrometer was set at 11.00 mm as the starting point and after counting 50 fringes entranceway the field of view, the reading of the micrometer was 11.07 mm. Since the smallest unit of measurements was 0.01 mm or 10 m, the uncertainty of this readings was assumed to be 5 m. It was noted that since the micrometer was committed to the mirror through a 51 lever, the actual displacement of the mirror was one fifth of this reading.Then, equation (6) was used to calculate the wavelengthTo calculate the uncertaintiesThe known value of the wavelength of this green light, 546.1 nm is within the errors of this measurement and a 2.5% difference was seen between the known and measured values which is a comparatively small error.A similar procedure was carried out to measure the average wavelength of the dichromatic light. Once again, the point of 11.00 mm was selected as the starting point and a fter counting 50 fringes, the finishing point was again very close to 11.07 mm. Then, by applying the same calculation method the value for measured wavelength and its uncertainty were found.Similarly, the actual known values for this light, 589.0 nm and 589.6, are within the bounds of uncertainty and show a 5% difference from the measured value.As the next step, in order to find the difference between the two present wavelengths in the light, the distance between two minima points in the beating phenomenon was measured. The point of minima was found by looking at the fringes and choosing the point that the fringes were the least visible. The two consecutive readings from the micrometer for the minima points were 15.15 mm and 16.62 mm.Using equation (14) and putting the measured value for wavelength The uncertainty in this calculation can be found fromAnd the known value of this difference, 0.6 nm, is within the range of uncertainty.Some of the sources of error in this measurements include the accuracy of the micrometer, the backlash of the micrometer, the quality of the mirrors and their respective reflection coefficient. Another issue with the Michelson interferometer is that the width of the fringes are relatively broad(a) and that makes this device less accurate. Using a similar concept, Fabrey and Perot introduced a new interferometric device in 1897 that could improve some of the issues observed in Michelson interferometer. Simply, in Fabrey-Perot interferometer the light passes through a pair of parallel mirrors and undergoes multiple reflection and the interference of these light rays creates highly well-defined interference fringes.The main value of this new interferometer was that the fringes were significantly thinner and this meant higher accuracy in measurement and resolving ability. As an example, FIG. 4 compares the monochromatic and dichromatic fringes observed each of the Michelson and Fabrey-Perot interferometers. It is evident that the bro ader fringes in Michelson interferometer results in the dichromatic fringes in (b) being undistinguishable.ConclusionsThe Michelson interferometer was investigated and its working concept and two sample applications of this device were practically examined. The wavelength of the green light produced by the Hg lamp was measured using this interferometer to be 560.040.4 nm which was close to the actual value of the wavelength, 546.1 nm, and with only a 2.5% difference between the experimental and known value. As another example application, the difference in the two present wavelengths in a yellow light produced by a Na lamp were measured and the beat phenomenon was observed. The difference was found to be 0.5330.077 nm and was very close to known value of 0.6 nm.The accuracy of the micrometer, the backlash in micrometer, the quality of the mirrors and the splitters were discussed as some of the possible sources of error in measurements. It was also pointed out the breadth of the frin ges in Michelson interferometer is one of the inherent causes of limited accuracy of this interferometer. Finally some sample results from Michelson and Fabry-Perot interferometer were compared to further show the inaccuracy of Michelson interferometer in measuring two very close wavelength in a dichromatic light.References1 electronic mail emailprotected2 http//www.egr.msu.edu/me/