PHYS 226 Experiment 4 The Interference and Diffraction of Light PDF

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Gong 1 Lise Gong 40102604 PHYS 226 Experiment #4: The Interference and Diffraction of Light Introduction The objective in “Experiment #4: The Interference and Diffraction of Light” is to see the qualitative effect of the interference and diffraction of a laser light beam. By observing the diffraction of a slim obstacle (lead & hair) & 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 a hair. In theory, 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. Diffraction results from the interference of an infinite number of waves emitted by a continuous distribution of source points. Our experiment requires us 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:

Equation 6 will be used to represent the experiment for Part 1: Diffraction of a Slim Obstacle. Y min  will be 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 pdf), L  is the distance between the apparatus and the wall, and a  is the width of the hair/lead.

Gong 2 In Part 2, we will be measuring the resulting light pattern of a double slit, which can be represented with equation 12

Here, 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. The expected results from the lab should follow a positive linear slope in Graph 1 & Graph 2. Equation 6 should represent the experiment well and show that the position of the minimum (y min) should be proportional to the minimum’s order m. The expected value of a should be approximately around 17 to 180 micrometers1 as it represents the width of a hair, and should be approximately 0.5 mm for the lead since that is the width stated by its manufacturer. For Graph 3, which is expected to be represented by equation 12, we should see that the position of the maximum y max is proportional to the maximum’s order. The expected d  is estimated to be around 0.5 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)

1

m

1.00E+0

±

1E-1

𝜆 (m)

6.60E-7

±

3E-8

L (m)

1.55E+0

±

8E-3

y min

4.45E-3

±

1E-4

a (m)

2.30E-4

±

2E-4

https://www.sciencenewsforstudents.org/blog/eureka-lab/measure-width-your-hair-laser-pointer

Gong 3 Table 2: Analysis for Lead Diffraction Pattern (Single Slit) m

1.00E+0

±

1E-1

𝜆 (m)

6.60E-7

±

3E-8

L (m)

1.55E+0

±

8E-3

y min

1.65E-3

±

1E-4

a (m)

6.20E-4

±

2E-4

Table 3: Analysis for Double Slit Lead Diffraction Pattern m

1.00E+0

±

1E-1

𝜆 (m)

6.60E-7

±

3E-8

L (m)

1.55E+0

±

8E-3

y max

1.75E-3

±

8E-5

d (min)

5.85E-4

±

3E-4

Gong 4

* for all graphs m is used for meter and m i s used for minimum order m *

Gong 5 Discussion The expected trendline of “Graph 1: Single Slit Diffraction Pattern for a Human Hair” should have followed equation 6, in which the position of the minimum (y min ) should be proportional to the minimum’s order m . As we observe our own data and its trendline on Graph 1, we can see that there is indeed a positive linear trendline of 0.00445 ± 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 0.000230 ± 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 0.230 ± 0.2 mm, which is in the range for average human hair width. For the lead, the diffraction pattern was expected to also be exemplified by equation 6, therefore we should see a positive linear trendline of the data points for Graph 2. Graph 2 shows overlapping uncertainties of the data points, therefore it can be said that the resulting graph is in agreement with the expected graph. The slope is 0.00165 ± 0.0001, showing a positive, linear relationship between the minimum order and the position of the minimum (y min), and reinforcing our expectations for Graph 2. The expected value for a  (lead width) is 0.5 mm as it is the stated width from the manufacturer. Our resulting a f or this diffraction pattern is 0.000620 ± 0.0002 m or 0.620 ± 0.2 mm, which is in agreement with the expected value since the uncertainty range includes the expected value. Lastly, the double slit apparatus expected the diffraction pattern to follow equation 12, meaning that the position of the maximum (y max) should be proportional to the maximum’s order m. As seen 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

Gong 6 resulting slope, 0.00175 ± 0.00008, was used to calculate the distance d b etween the slits and its uncertainty. The resulting value of d i s 0.000585 ± 0.0003 m, which makes sense given the geometry of my setup. This value can be said to be in agreement with the expected d, b ecause their uncertainty ranges overlap. Experimental errors in the 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 I found was an estimated average of all human hair diameters and may not be an accurate reference. Additionally, 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. The main source of error is the distance between the laser and the wall, and the size of the dots, there is possibility to further enlarge the dots due to attenuation as it passes through the air. The apparatus of this experiment could have been improved if it were executed in a vacuum.

Conclusion All in all, 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 the laser experiment, we are able to determine the diameter of my own hair, which was 0.620 ± 0.2 mm by using diffraction principles. The slit difference found is 0.000585 ± 0.0003 m, which makes sense given 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.

Gong 7 References (1) “Diffraction and Constructive and Destructive Interference (Article).” Khan Academy , Khan Academy, www.khanacademy.org/test-prep/mcat/physical-processes/light-and-electromagnetic-radiation-q uestions/a/diffraction-and-constructive-and-destructive-interference. (2) Diffraction and Interference . electron6.phys.utk.edu/phys250/modules/module%201/diffraction_and_interference.htm. (3) Duncan, Chuck. Interference and Diffraction of Light , KET Virtual Physics Labs, www.webassign.net/question_assets/ketphysvl1/lab_16/manual.html....