Lamia phy226 lab 4 pdf - CONCEPT PDF

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EXPERIMENT #4: THE INTERFERENCE AND DIFFRACTION OF LIGHT PHYS 226

Lamia Tasnim 40076908 | 23/03/2021

Tasnim L. Introduction Our objective in this lab “The Interference and Diffraction of Light” is to see the qualitative effect of the interference and diffraction of a laser light beam. So, by observing the diffraction of a slim obstacle (lead & hair) and by using diffraction principles and the distance between two slits using the interference of light passing through two slits, we will be able to determine the width of the hair and lead. Theoretically, diffraction occurs “when light passes through an obstacle in its path, this allows the light source to behave like multiple coherent light sources which will interfere with one another”. The results of diffraction from the interference of an infinite number of waves emitted by a continuous distribution of source points. This lab requires to find the width of a hair, using an equation that describes the position of the light intensity minimum “where destructive interference occurs (no light)”. This is the main characteristic of the light intensity pattern, and can be written as equation 6 (from lab manual):

Equation 6 will be used to represent the experiment for Part 1: Diffraction of a Slim Obstacle. Y min is used to demonstrate the slope of our graph, m is the minimum’s number, 𝜆 is the wavelength of the laser pointer (given 660 ± 30 nm in instruction manual), L is the distance between the apparatus and the wall, and a is the width of the hair/lead. In Part 2, we will be measuring the resulting light pattern of a double slit, which can be represented with equation 12 (from lab manual):

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For this we are expected to observe a series of maximums (bright spots) with the same width. Y max represents the slope of the graph, m is the maximum’s number, d represents the distance from the centre of one slit to the centre of the next. Our expected results from this lab should follow a positive linear slope in Graph 1 & Graph 2. Equation 6 should be able to represent the experiment well and show that the position of the minimum (y min) will be proportional to the minimum’s order m. The expected value of a should be approximately around 17 to 180 micrometers as it represents the width of a hair and a should be approximately 0.7 mm for the lead since that is the width stated by its manufacturer (couldn’t obtain 0.5mm). As for Graph 3, which is expected to be represented by equation 12, we should be able to see the position of the maximum y max is proportional to the maximum’s order. This expected d is estimated to be around 0.7 mm since it measures “the distance between the slits and should follow the geometry of the setup”. Results

Table 1: Analysis for Hair Diffraction Pattern (Single Slit) m 1.00E+00 ± 1.00E-01 6.60E-07 ± 3.00E-08 ! (m) L(m) 2.79E+00 ± 8.00E-03 y(min) 1.31E-02 ± 1.00E-04 a (m) 1.41E-04 ± 2.00E-04

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Table 2: Analysis for Lead Diffraction Pattern (Single Slit) m 1.00E+00 ± 1.00E-01 6.60E-07 ± 3.00E-08 ! (m) L(m) 2.79E+00 ± 8.00E-03 y(min) 2.40E-03 ± 1.00E-04 a (m) 7.68E-04 ± 2.00E-04

AVERAGE DISTANCE FROM CENTRAL MAXIMUM (M)

Table 3: Analysis for Double Slit Lead Diffraction Pattern m 1.00E+00 ± 1.00E-01 6.60E-07 ± 3.00E-08 ! (m) L(m) 2.79E+00 ± 8.00E-03 y(max) 2.49E-03 ± 8.00E-05 d (min) 7.42E-04 ± 3.00E-04 DOUBLE SLIT DIFFRACTION PATTERN FOR A 0.7MM LEAD PIECE 2.50E-02

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y = 0.0025x + 0.0025 R² = 0.9981

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MINIMUM ORDER M Length from m=0 (M)

Linear (Length from m=0 (M))

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AVERAGE DISTANCE FROM CENTRAL MAXIMUM (M)

GRAPH 1: SINGLE SLIT DIFFRACTION PATTERN FOR A HUMAN HAIR 1.00E-01 9.00E-02 8.00E-02 7.00E-02 6.00E-02 y = 0.0131x + 0.0072 R² = 0.9849

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AVERAGE DISTANCE FROM CENTRAL MAXIMUM (M)

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GRAPH 2: SINGLE SLIT DIFFRACTION PATTERN FOR A 0.7MM LEAD PIECE 1.80E-02 1.60E-02 1.40E-02 1.20E-02 y = 0.0024x + 0.0003 R² = 0.9947

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MINIMUM ORDER M Length from m=0 (M)

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Tasnim L. Discussion Our expected trendline of “Graph 1: Single Slit Diffraction Pattern for a Human Hair” should follow the equation 6, in which the position of the minimum (y min) should be proportional to the minimum’s order m. By observation of our own data and its trendline on Graph 1, we can see that there is indeed a positive linear trendline of 0.0130 ± 0.0001. Using this value for y min, we can plug it back into equation 6 and solve for a. Our expected value for a was 17 - 180 micrometers or 0.000017 to 0.000180 m, and the result from our experiment for a (hair width) is 0.000141± 0.0002 m. The two measurements are said to be in agreement, since the uncertainty range overlaps the expected value. This means our hair width is 0.141 ± 0.2 mm, which is in the range for average human hair width. The lead, the diffraction pattern was expected to also be followed by equation 6, therefore we should see a positive linear trendline of the data points in Graph 2. Graph 2 shows overlapping uncertainties of the data points: so, it can be said that the resulting graph is in agreement with the expected graph. The slope is 0.0024 ± 0.0001, showing a positive, linear relationship between the minimum order and the position of the minimum (y min). The expected value for a (lead width) is 0.7 mm as it is the stated width from the manufacturer. Our resulting a for this diffraction pattern is 0.000768 ± 0.0002 m or 0.77 ± 0.2 mm, which is in agreement with the expected value since the uncertainty range includes the expected value. Finally, the double slit apparatus expected the diffraction pattern to follow equation 12, which means that the position of the maximum (y max) should be proportional to the maximum’s order m. We see in Graph 3, the data points form a positive linear trendline, demonstrating the proportional relationship between the position of the maximum and the maximum order. The resulting slope, 0.0025 ± 0.00008, was used to calculate the distance d

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Tasnim L. between the slits and its uncertainty. The resulting value of d is 0.000742 ± 0.0003 m, which makes sense given the geometry of the setup. This value can be said to be in agreement with the expected d, since their uncertainty ranges overlap. Experimental errors we see in this experiment may be due to the fact that the diameter of a human hair does not have a standard value since different people have different hair structures. The “standard” value which was an estimated average of all human hair diameters could be an inaccurate reference. Furthermore, the marking of the bright spots when measuring the distance between the central maximum and the dark spots on each side can be prone to systematic errors. One of the main sources of error is the distance between the laser and the wall, plus the size of the dots. Conclusion To conclude, we were able to observe the qualitative effect of the interference and diffraction of a light beam through a single and double slit diffraction. Through this experiment, we are able to determine the diameter of a strand of hair, which was 0.141 ± 0.2 mm by using diffraction principles. The slit difference found is 0.000742 ± 0.0003 m, which is accurate given to the geometry of the setup and how narrow the slits were formed around the lead. All of expected values can be said to be in agreement with the results, as their uncertainty ranges overlap.

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Tasnim L. References Diffraction and Interference. electron6.phys.utk.edu/phys250/modules/module%201/diffraction_and_interference.htm. Duncan, Chuck. Interference and Diffraction of Light, KET Virtual Physics Labs, www.webassign.net/question_assets/ketphysvl1/lab_16/manual.html. “Diffraction and Constructive and Destructive Interference (Article).” Khan Academy, Khan Academy, www.khanacademy.org/test-prep/mcat/physical-processes/light-and-electromagneticradiation-q uestions/a/diffraction-and-constructive-and-destructive-interference. http://www.sfu.ca/~mxchen/phys1021003/P102LN31B.pdf Vedad, Farhad. (2019). Diffraction and the speed of light A new concept by Farhad Vedad.

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