Lab report 1

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University of Akron *

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Physics

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Jan 9, 2024

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Shanieka Banks Lab Partner: Ezra TA: Lei Liu Lab Section: 014 Experiment Date: 9/18/23 Title: Interference and Diffraction Abstract: This lab showed how interference and diffraction wave patterns were created using both single and double slit apparatuses. A laser was passed through both the single and double slits and the resulting patterns were measured and used to calculate the wavelength (λ). For the single slit apparatus three patterns were used: B, C, and D. Through calculation the following wavelengths were obtained: pattern B, λ= 596 nm, pattern C, λ= 625 nm, and for pattern D, λ= 756 nm. The average wavelength was then calculated for those three patterns: average λ= 659 nm. For the double slit apparatus only two patterns were used: B and C; the wavelengths were calculated yielding the following results: pattern B, λ= 719 nm and pattern C, λ= 637 nm. Introduction & Theory: The purpose of this lab was to be able to explain how interference and diffraction wave patterns are created using both the single and double slit apparatuses; this was done with the use of a laser. In order to measure and calculate the wavelength of the laser it was passed through the single and double slit apparatuses; the widths used for calculations were known/provided. For both the single and double slits, the laser was passed through the apparatus and the space of interference minima/maxima produced on the distant screen was measured. Interference is defined as the interaction of two or more electromagnetic waves resulting into one in which the displacement is either reinforced (constructive interference) or canceled (destructive interference). Constructive interference occurs when the peaks of a wave cross over each other; destructive interference occurs when two waves overlap so much that they cancel each other out. Diffraction is described as a process where a beam of light or other system of waves is spread out due to being passed through a small opening or across an edge. Figure one illustrates a monochromatic light being passed through a single slit. 1
For this lab destructive interference was observed so the equation used to calculate wavelength (λ) for the single slit apparatus was: ( 1 ) y m = m λ D b ,m = 1,2,3,.. . where y m is defined as the distance to the m-th minimum (from the central intensity maximum to an intensity minimum). m is defined as 1, 2, 3, …, λ is defined as the wavelength, D is defined as the distance from the laser to the screen, and b is defined as the given slit width. Figure 2. Single slit projection on screen To obtain the wavelength equation was then rearranged to solve for λ: ( 2 ) λ = y m b mD The equation used to calculate wavelength (λ) for the double slit apparatus was: ( 3 ) y n = n λ D d ,n = 1,2,3,.. . where y n is defined as the distance to the n-th minimum (from the central intensity maximum to an intensity minimum). n is defined as 1, 2, 3, …, λ is defined as the wavelength, D is defined as the distance from the laser to the screen, and d is defined as the given slit width. 2
Figure 3. Double slit projection on screen To obtain the wavelength equation was then rearranged to solve for λ: ( 4 ) λ = y n d nD To be able to calculate the angles defined by θ, as seen if Figures 2 and 3, for both the single and double slits the following equation would be used: ( 5 ) sinθ = y D Procedure: Single slit: 1. Adjust the laser so that light passes through one of the single slits, the width is given. 2. Let the light fall on a screen a known distance D at least 50 cm away from the slit, record the distance. 3. Measure the distance y m from the central intensity maximum to an intensity minimum, the further this minimum is from the central maximum, the more accurate your result will be. 4. Record the distance and the order, m, of the minimum; with this distance and the distance of your screen from the slit, calculate the angle at which the intensity is at a minimum using equation (5). 5. Calculate and record the wavelength of the laser using equation (4). 6. Repeat for two other known slit widths. Find and report the average wavelength. 3
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