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The application experiment of diffraction grating Stage 2 Physics Physics May, 2017 by Yusi Yan (Ashley) Jayu Chen (Cecilia) Background: Diffraction is a change in the direction of propagation of a wave as it passes by an obstacle while remaining in the same medium. In the other words, it is bending of waves around obstacles, or spreading of waves by passing them through an aperture, or opening. (BBC 2014) Diffraction of light is used widely in applications of science and technology in the daily life. For example, productions of holograms which make use of laser beams that mix at an angle, producing an interference pattern of alternating bright and dark lines is an application of the theory of diffraction grating. In this case, holograms are used on credit cards or other identification cards as a security measure, providing an image that can be read by an optical scanner. In addition, Xrays which is used in the hospital to check patients’ body is another application of diffraction lights. This experiment is related with some other theories which have been studied before, such as the energy of wave sources, the electromagnetic waves or fields, the characteristics of lights, and some basic mathematic information (sine, cosine, and tangent). And there are two functions need to be known, and d sin θ = mλ .Furthermore, the graph below shows a basic image of the theory of diffraction. (http://imgarcade.com/diffraction-grating.html) Variables: Independent variables: The distance between the CD and the A4 white paper is the independent variables. Dependent variables: The distance between two points on the two sides of the central maximum is the dependent variable. Constants: The wavelength of Red laser which is equal to 632.8nm will never change. The industry standards for CD which is 1.6 will also never change. Safety consideration: Source of the hazard Potential outcomes Red laser It is likely to break experimenters’ Wear the safety glasses during the whole experiment. eyesight, or even make experimenters blind 1 meter ruler It is likely to hurt other people for Pay more attention when doing the the long length. measurements. Electric power The leakage of electricity will take a risk of people’s health, or even lead the death. Experimental setup: The graph is the setup image for part B: Control measures Be electrically checked before the experiment. Screen Laser y CD Results: Case 1 Case 2 Point A (cm ) (4.45, 5.8) (0.32, 8.8) Point B (cm ) L (cm ) (1, 8.75) 13.8 (2, 5.2) 13.8 (cm ) 4.54 3.95 Case 3 (4.5, 5.90) (1.4, 8.55) 4.09 13.8 (°) 0.312 0.276 0.284 Analysis: From the basic information which has been learned, the function is given. Then the angle can be calculated out. Where is the distance between two points found between the central maximum. L is the distance between the A4 white paper and the CD. In this experiment, the line is not on the horizontal direction, so the distance is calculated by the function In case 1, = As a result, , and m=1, =632.8nm=6.328 From the function that cm , and in this case, m So d= In case 2, As a result, = , and cm From the function that , and in this case, m=1, =632.8nm=6.328 m So d= In case 3, = As a result, , and case, m=1, =632.8nm=6.328 cm From the function that , and in this m So d= m The average value of d= Evaluation: Precision: By the calculation, ％error=(1 − average value 2.16μm 1.6μm 1.6μm ) × 100％=(1 − )× 100％=35％ The results of precision are not very well because the error percentage is too large. This kind of problem is resulted from the random errors, and in the next part will look at the random errors. Random errors: In this experiment, experimenters need to guess values for measurements if the reading number is not exactly on the limit line. In this case, the gap between the real value and the result measured by experimenters is increased easily. Furthermore, the line which is reflected by the CD is not a horizontal line, and the distance of measured is a little different from the real value. If it is not a horizontal line, experimenters may need to measure the vertical distances and the horizontal distances, and calculate the length by the way named Pythagorean Theorem. As a result, experimenters had better to make the line parallel to the horizontal axis when setting up the location of the CD. Accuracy: biggest value−smalleast value 2.29−2.03 0.26 By the calculation, ％range= average value = 2.16 = =12 ％ 2.16 This value is a little bit close to 10 ％, and the accuracy of this experiment seems to be acceptable. Systematic errors are factors which can affect the accuracy of the experiments, and there is some analysis of systematic errors in the following part. Systematic errors: When observing the image reflected on the paper, the image graph is related to the surface of the CD. If the surface of the CD is impossible to be extremely smooth, the reflected image will not be a horizontal line to the table and the measurement of distance will also be affected. As a result, the distance ) which is calculated by the Pythagorean Theorem needs to be estimated to 2 or 3 significant figures. In this case, the final result will not be close to the real value. When reading the values, some values are not exactly on the scale, and experimenters may use an approximate number by guessing as the final result. In this case, the final result will not equal to the value in real, so the conclusion can be affected. Finally, the white A4 paper is likely to have the bending deflection, and the equipment may affect the results of the experiment because the plane of reflection is not flat Improvements: To reduce the effects caused by the surface of the CD to the result, experimenters can choose some CDs with a better ability of reflection, or clean the face of reflection to move away the ash before the experiment. After the reflection, experimenters need to move the location of CD to make sure the line is in the horizontal direction. To reduce the gap between reading values and the values in the real, experimenters should measure a value for more times, and calculate the average value as the result. To make the plane of reflection flat enough, experimenters can use a screen, instead of a piece of white A4 paper. Conclusion In this experiment, the results are calculated by the measurements and the values are not extremely close to the real values. ％error=(1 − average value 2.16μm 1.6μm 1.6μm ) × 100％=(1 − )× 100％=35％ biggest value−smalleast value 2.29−2.03 0.26 ％range= average value = 2.16 =2.16=12 ％ From the calculations above, the experiment is not finished extremely well. There are several reasons for this situation. Firstly, the line reflected on the paper is not a horizontal line, so the measurements seem to be more likely to be away from the real values. In this case, the accuracy and the precision are both well because there are not any extremely large or small values as well. In the final calculation, the functions of have been and proved by three pieces of data. The final value of d is around 2.16 , and it is close to the real value 1.6 . As a result, the aim of this experiment is approximately achieved. Reference: https://www.lasercomponents.com/uk/product/diffraction-grating/ http://imgarcade.com/diffraction-grating.html