AllisonSmith_lab9

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Dec 6, 2023

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Allison Smith alsmi911@vols.utk.edu Lab 9 GOAL : The goal of this lab is to experimentally determine the width of a single slit and the spacing of two slits using diffraction and interference patterns, while also measuring the diameter of a hair through the principles of diffraction. Part 1 : Observe and analyze a single slit and multiple slit diffraction patterns (a) Drag the single slit slide into into the path of the laser beam. The slit width w is 20 μm. Observe the diffraction pattern. Dark fringes in the diffraction pattern of a single slit are found at angles θ for which w sinθ = mλ, m = 1, 2, ... . To see a well-resolved pattern, use a large distance between the slit and the screen.  Verify the slit width w. Explain which measurement you made, show your calculation and your result for the slit width. There are several measurements you can make. Pick one. I used w sin  = m  to confirm the slit width. We can simplify the expression to w=  /sin  since m = 1. The wavelength is provided, the angle is calculated to be 0.3165 radians, and the equation confirms that w = 20  m when all the numbers are entered. (b) Drag the double slit slide into into the path of the laser beam. Each slit is w is 20 μm wide. Constructively interference at angles θ such that d sinθ = mλ, m = 0, 1, 2, ... .  Determine the slit spacing d. Explain which measurement you made, show your calculation and your result for the slit spacing. There are several measurements you can make. Pick one. (Hint) I utilized the method d sin  = m  to find split spacing d using the 2-slit piece, but I had to rearrange it to d=m  /sin  because L=1m. I then got d=0.05m by substituting 0.716 for the sin  and 633nm for the wavelength. (c) Drag the slide with four slits into into the path of the laser beam. Again each slit is w = 20 μm wide.

 As you observe the pattern, does it differ from that of the double slit for the same slide to screen distance L? If yes, what is different? (Zoom in to get a better view.) Yes, there is a difference in the pattern. When I glanced through the 4- slit piece, there seemed to be more gaps and dark spots. Part 2 : Measure the thickness of a hair  Observe the diffraction pattern on the screen. Determine the diameter w of the hair. Explain which measurement you made, show your calculation and your result for the diameter of the hair. I used diameter =  md/sin  to get the hair's diameter. I took a measurement from the center bright maxima to the left first-order maxima in order to calculate sin. I received a value of 6.25. Entering values yields diameter = (.633) (.00625)/sin (0.12499), which gives me 0.003mm as the hair's diameter. REFLECTION : As a student completing this lab, I found it to be a fascinating and engaging exploration of the fundamental phenomena of diffraction and interference. The hands-on experience and simulation allowed me to visualize and understand how light behaves when passing through slits and interacting with objects like a human hair. Through the lab, I gained practical insights into the concepts of wavelength, slit width, and slit spacing, and I appreciated the importance of these principles in understanding the behavior of light. The ability to measure these parameters by observing patterns was an eye-opening experience, highlighting the precision and subtlety of optical phenomena. Furthermore, the lab provided a real-world application by allowing me to measure the diameter of a hair using the principles of diffraction. This aspect of the experiment showcased the practicality of optical science and its relevance to everyday life. Overall, this lab was a valuable learning experience that reinforced the theoretical knowledge I had gained about diffraction and interference, and it deepened my appreciation for the intricate and beautiful world of optics. It underscored the importance of experimentation and observation in the scientific process and left me with a newfound curiosity about the behavior of light.

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