Diffraction and Interference Essay Example for Free

Diffraction and Interference EssayPurpose The aim of doing this experiment was to examine diffraction and interference effects of put down short-lived through various apertures, and use the diffraction patterns obtained by single and double slit apertures to find the wavelength of the light lineage used. Theory We know that light feces be described by two theories, namely the particle theory and the wave theory of light, each having its own experimental proofs. In this experiment, we examine the interference and diffraction phenomena of light, twain of which can be described by the wave theory of light. While interference is just the superposition of waves, diffraction is also any deviation from geometrical optics that results from the restriction of a wavefront of light. In other words, diffraction is aiming the double-slit experiment by taking into account the width of the slit openings, too. A nonher way of distinguishing betwixt interference and diffraction is to co nsider the interfering beams in diffraction phenomena as originating from a continuous distri moreoverion of sources, whereas the interfering beams in interference phenomena as originating from a discrete number of sources.This way of interposition of interference and diffraction is a result of Huygens principle which states that every plosive speech sound of a given wavefront of light can be considered a source of subsidiary spherical wavelets. Hence, superposition occurs betwixt these secondary waves emitted from antithetical parts of the wavefront, taking into account both their amplitudes and phases. Diffraction effects can also be classified jibe to the mathematical musical themes used in calculations. In the case of the light source and the observation screen being very farther from the slit, relative to the slit width, the hazard and diffracted waves are assumed to be plane and the diffraction type is called Fraunhofer, or far-field diffraction.In this case, as the v iewing screen is moved relative to the aperture, the size of the diffraction pattern changes, but not the shape. We are going to use this kind of approximation in this experiment. We should keep in mind that the Huygens principle used to find the diffraction transaction is itself an approximation. When reason the single-slit Fraunhofer diffraction a rectangular aperture with a length much larger than its width is considered. In this case the vividness of the light reaching the screen at point P, at an tip off is given by Is=I0(sin22)where=12kasin=asinIn the above relations I0 is the intensity at the middle of the central maxima and a is the slit width. Hence, by taking the limit as 0, we line up that this pattern attains its maximum at =0. Similarly, equating =m, we obtain the minima of the pattern and we get the following relation for this case n=asinwhere n=1,2,3, For small angles we can make the sin=tan approximation and, calling L the distance between the slit and the scree n, we can get y=Lsin, where y is the distance from the central maximum to the observation point. For this case, we conclude that on the screen, the irradiance is a maximum at =0, hence y=0, and it drops to zero at value of y such that y=La . Therefore, we can find using this relation. (Here, y is the fair distance between adjacent minima).When we regard the double-slit diffraction we see that we deem to do with two different terms, one of which belongs to the interference pattern, and the other to the diffraction pattern. If we ignore the effect of the slit widths, we get the intensity of the pattern given by further the interference term as I=4I0cos2, where =(b)sin. Here, is the angle of observation and b is the slit separation. Nevertheless, since the intensity from a single slit depends on the angle through diffraction, we should take into account the diffraction pattern, too. Now, the intensity is given by I=4I0(sin22)cos2In this case is again =12kasin=asin. Hence, we con clude that in double slit diffraction the intensity is the product of the interference and diffraction patterns. By analyzing the intensity relation, we observe that an interference minimum occurs whenever =(n+1/2) for n=0,1,2,3,, and an interference maxima occurs whenever =n, again for n=0,1,2, Using the approximation sin=tan, we obtain y=Lsin, and y=Lb, where y is the average distance between either adjacent maxima or minima.Data and Results Part A Single SlitPattern A B CWidth of the slit, a 410-5m 810-5m 1610-5mDistance slit-screen, L 1m 1m 1mAverage dist btw minima, y 1.67 cm 0.75 cm 0.45 cm=ay/L 668 nm 600 nm 720 nm misconduct y on y 0.08173 cm 0.138 cm 0.0548 cmError on =ay/L 32.7 nm 110 nm 87.7 nm= 635.5 nm 710 nm 632.3 nm y1 y2 y3 y4 y5 y6A 1.8 1.6 1.7 1.7 1.6 1.6B 0.5 0.8 0.8 0.8 0.9 0.7C 0.5 0.5 0.5 0.4 0.4 0.4The error on y is comprise using the relation belowy=i=1N(yi-y)N-1Part B Double SlitPattern D E FWidth of the slit, a 810-5m 810-5m 410-5mSlit separation, b 510-4 m 2.510-4m 2.510-4mDistance slit-screen, L 1m 1m 1mAverage dist btw minima, y 0.00160 m 0.00300 m 0.00155 m =by/L 800 nm 750 nm 387.5 nmError y on y 0.000342m 0.000524m 0.000342mError on =by/L 171 nm 131 nm 85.5 nm= 629 nm 619 nm 473 nmy D E F1 0.138 0.110 0.0532 0.141 0.106 0.0513 0.143 0.101 0.0484 0.146 0.095 0.0455 0.148 0.090 0.0436 0.151 0.086 0.0407 0.154 0.0388 0.156 0.0359 0.033We calculated the difference between each successive data to obtain the displacement. Then, we multiplied each displacement value with a factor of (21.5/34.5) because the scale of the linear translator and the interface were not equal. Having done this we calculated the average distance. The error on y is found again by using the relationy=i=1N(yi-y)N-1Discussion and destination In part A we considered interference and diffraction pattern of a single slit opening for three different slits. We measured the distance between the source and the slit to be 1m and we used the relations found in the t heory part in order to find the wavelength of the light source used. We found the average distance between minima to be 1.67 cm for slit A, 0.75 cm for slit B and 0.45 cm for slit C. Hence, we found the wavelength of the light source to have determine of 668 nm for slit A, 600nm for slit B and 720nm for slit C. However, after calculating the error in the average distance and using this error, the wavelengths turned out to be 635.5nm for slit A, 710nm for slit B and 632.3nm for slit C. We know that theoretically the wavelength is expected to be 65010nm. Our experimental values, despite the fact they are close to, do not fit totally to the expected theoretical ones.Hence, we argue that any discrepancy in the values found is a result of the imprecise equipment used, especially the light sensor. Furthermore, we claim that these discrepancies are also a result of the fact that we had to move the linear translator with our hand slowly enough so that the find outor could detect the inten sity peak and the other maxima. Hence, it is very much likely that we could not carry this process out precisely enough as it is required in order to have correct data, since we are human beings and it is impossible for us to achieve such a thing. We also think that the light coming from the border might have had a negative effect on our results since the room where the experiment was carried out was not evacuated well enough. Moreover, we point out that the relations between wavelength, distance between minima and slit width used to find the wavelength and the Huygens principle itself are all approximations, since as it was stated in the theory part, we used far field mathematical approximations in order to obtain these relations.In part B, we used a double slit opening in order to observe the interference and diffraction pattern. In this case both the slit width and the slit separation have an effect when finding the intensity at a legitimate point. However, in the relations use d to find the wavelength we considered only the slit separation b. In this part, after calculating the error in displacement and using this in , we found the wavelength values to be of 629nm for slit D, 619nm for slit E and 473nm for slit F. We observe that, except for slit F, these values of agree with the values found in part A. We claim that the discrepancies in this part are a result of the same reasons causing the discrepancies in part A. As for the case of slit F where turned out to be 473nm (much smaller than the theoretical value) we think that the main reason for such a result is the change in width of the slit, which in this case, unlike the other two cases, is 0.04mm. This leads us to conclude that, as expected theoretically, the width of the slit also affects the intensity pattern, and in these cases more precise relations should be used in order to obtain correct data.Applications Interference and diffraction phenomena of light have found a quite large application in science and technology. Understanding these phenomena has led to apprehension the world nigh us and being able to use it in a better way in order to fulfill our needs. Among the most important applications of diffraction for example, is the fact that it is used to obtain accurate information about the atomic scale structure of the matter around us. Since the number of atoms or molecules inside a crystal is arranged in such a way that it resembles a grating with very thin spacing,diffraction phenomena leads to understanding the insights of each crystal structure.Diffraction phenomena was also used to learn that the sodium and chloride ions are bonded in a lattice fashion and not molecules, to distinguish between different cubic lattice, to analyze all kinds of materials, even biological samples, etc. Using diffraction interesting things such as hair thickness can also be measured .The interference phenomenon, on the other hand, is used to make highly-wavelength specific mirrors for lasers. Furthermore, interference is the reason why soap bubbles appear colorful. Many other opthalmic coatings owe their optical properties to the interference phenomena. An example of this is the antireflection coatings on lenses that we use everyday. Another application of interference is holography, which is a way of reconstructing three dimensional images with laser light.mayhap the most fascinating application of interference is to create holograms. This is done by reflecting a coherent light source, such as a laser, off of an fair game onto a special film. The interference patterns created by the reflected light are what result in the holographic image, which can be viewed when it is again placed in the overcompensate sort of lighting. Moreover, diffraction and interference can be observed when an atom passes through a standard light wave and its position is localized. In this case, the localization can be thought of as the creation of virtual slits leading to the above me ntioned phenomena. Diffraction is also used to understand the insights of the ionosphere. All in all, by doing this experiment we learn the importance of the phenomenon of interference and diffraction in our lives.Referenceshttp//online.physics.uiuc.edu/courses/phys214/spring09/Lectures/Lect04.pdf http//bigbro.biophys.cornell.edu/toombes/Science_Education/Laser_Diffraction/Diffraction_Lesson.pdf http//answers.yahoo.com/question/index?qid=20080509124425AAyW8bl http//physics.about.com/od/mathematicsofwaves/a/interference.htm URL http//link.aps.org/doi/10.1103/PhysRevLett.68.472