Lab 9 Retake

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Dec 6, 2023

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Temple University College of Science and Technology Physics Department Physics 1022 Section 052 Lab 9 Interference and Diffraction

Lab 9: Interference and Diffraction 11/3/2023 Group Members Group 65: Cynthia Klingensmith Goals This week’s experiment is designed to demonstrate that white light contains all the colors of the visible spectrum and to explore the reasons behind the colors of objects. We will use our optics kit which includes a white light source to examine how light behaves when it passes through slit marks. Additionally, the kit will help in our understanding of the impact of slit size on diffraction patterns. While completing the lab, we should be able to determine polarizing the direction of light. Procedure Part 1: - Position the laser, the single slit wheel, and the screen on the optics bench according to the setup shown in the lab manual. - Position the laser so that is is directly against the diffraction slit wheel which should be set 30 cm away form the wheel. - Align the slit with the laser beam by rotating the wheel to the 9 o’clocl position as shown in the image. Adjust the wheel until the slit has a width of 0.08 mm. - Dim the room lights to observe the pattern more clearly. - Once the pattern is visible, ove the screen to a distance of 70 cm from the slit to make your observations. - Continue to rotate the slit disk wheel to examine different slit widths (0.02 mm, 0.04 mm, 0.08 mm. And 0.16 mm). Make sure to document observations for each width and reset the wheel to 0.08 mm when finished). - Calculat the distance on the screen by rearranging the given equation to solve for y as a function of the wavelength ( 𝛌 ), the distance (L), and the slit width (a). - Use the equation to calculate the predicted value of y for the first minimum by inserting the known values for 𝛌 , L, and a. Ensure that L is measured from the screen to the front of the slit wheel. Directly measure y by determining the full width of the central maximum using a ruler and then dividing that number by 2. - Determine the percent difference to evaluate the accuracy of the predicted value in comparison to the measured value.

Part 2: - Switch out the slit wheel with the multi-slit wheel. Adjust the laser alignment until we see two side-by-side patterns oriented vertically on the screen. - Observe how increasing the number of slits affects the pattern. Switch to the multiple slit section of the wheel. Cycle through the 2, 3, 4, and 5 slits and observe the patterns. Part 3: - The screen was set to 10 cm from the laser and the diffraction grating held was in front of the laser. - A meter stick was used to measure y value from the three different points and the value of our predicted and the actual was used to find the percent error. Error and Precaution The most important precaution for this experiment is making sure that we obtain accurate data. Some errors that can occur are human error, some measurements could be different from the perspective from which they are observed. Another precaution we need to look out for is environmental factors such as the outside source light could affect how we see the laser readings. The room could not be dark enough and this can affect how much white light we can see. Results Part 1: Slit Width (mm) Central maximum width (mm) 0.02 35 0.04 15 0.08 8 0.16 4.5 Calculations: m = 1 = 650 nm λ L = 0.7 m a = 0.08 mm Predicted y = m L/a = 1(650e-9)(0.7)/(0.08e-3)= 0.0057 m λ Actual y = 0.009 m % difference: {(|V1 - V2 |) / [(V1 + V2)/2]}* 100 = 44.9%

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Observations 0.02 Slit Width: 0.04 Slit Width: 0.08 Slit Width: 0.16 Slit Width Part 2 Single Slit vs. Double Slit

Part 3 Calculations y = 0.0043m (4.3 mm) L = 0.1 m (10 cm) m = 1 d = 0.000156 m λ = (0.0043 m) * (0.000156 m) / [ (1) * 0.1 m) ] λ = 670 nm Percent Error % error : 670 - 650 nm / 650 nm & error : 0.03 or 3% error Questions 1. How does the width of the central maximum change as you go to smaller and smaller slit widths? I observed that the central maxima was inversely proportional to the slit width. By reducing the size of the slit width, the central maxima increased in size. 2. How is the double slit pattern different from that of the single slit? Are the locations of the minima of the single slit still present in the pattern of the double slit? Why do you think this is so? Looking at the single slit, it produces a continuous line, where the double slit results in a line that has a dotted pattern. This occurs as the laser light passes through the double slit,

which allows for an even distribution which creates multiple local minima and maxima. On the other hand, the single slit creates only one central maximum. 3. How does the number of slits affect the sharpness or definition of the maxima in the multiple alit pattern? Are neighboring maxima well-defined? As the number of slits increases, a greater number of maxima are shown. They appear smaller in size which leads to a more pronounced pattern of the dotted lines. This also causes the diffraction patterns to be more declined due to the narrowness of the peaks. 4. What are the two big differences between this double-slit equation and the single-slit question? In the equation for single-slit diffraction, “a” represents the width of the slit. For double-slit diffraction, “d” represents the distance between the slits. Furthermore, for single-slits, “m” corresponds to the m-th order minima, while in the double-slit case, “m” refers to the m-th order maxima in the interference pattern. 5. Was your prediction correct? (It’s ok if not!) How did decreasing d by switching to the diffraction grating affect the separation distance and angle between neighboring maxima? My prediction was correct, as the distance between the slits increases, the smaller the angles formed while also increasing the distance from the central maxima. As a result, this increased the width of the diffraction pattern. 6. Which color has a smaller θ and is thus nearer to the central maxima: violet or red? Did this match your prediction? Violet light appears nearest to the central maxima due to its shorter wavelength. Since red light has a longer wavelength, it is the most distant from the central peak because the separation in the diffraction pattern increases proportionally with wavelength. 7. The ability of optical instruments to resolve two neighboring objects is limited by the very nature of light itself. Why do you think this limit of resolution is described as ‘diffraction limited?’ To answer this, imagine taking a photo of two very small point sources of light where the light from each source diffracts through the camera’s lens and produces a diffraction pattern on the film rather than a faithfully reproduced point.

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The resolution limit is constrained by diffraction due to the high frequency. This leads to a loss of sharpness, rendering images blurry and makes it difficult for the instrument observe the light. As a result, the images b lue into one another and it can be difficult to differentiate them. Discussion In this lab experiment, I investigated how white light undergoes interference and diffraction, and how it produces colors. In part 1, I observed the diffraction of a laser beam through a single slit. I tok note of the impact of the slit size on the central maximum and concluded that narrower slits formed broader, more proximal central maximum, while wider slits resulted in smaller central maximum. My calculations shwed a significant percent difference, likely due to imprecise measurements of “y” for the central maximum and the slit minima. For part 2, I compared single and double slits, seeing distinct differences such as the laser produced line patterns, solid line for single slit and a dotted line for double slit. This was consistent with the presence of a central maximum for single slit and multiple minima and maxima in the double slits. In part 3, I used diffraction grating to assess the wavelength of light, observing three distinct diffraction points with the laser. When introducing the diffraction grating to white light, I determined that violet and blue light since they have shorter wavelengths, were closer to the central maximum. The percent error in my experiment was 3%, with an experimental value of 670 nm fr the wavelength, closely aligning with the expected value of 650 nm.

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