x (m) 1.00 1.50 2.00 2.50 r (cm) 5.6 8.5 11.6 14.1
At the metal fabrication company where you work, you are asked to measure the diameter D of a very small circular hole in a thin, vertical metal plate. To do so, you pass coherent monochromatic light with wavelength 562 nm through the hole and observe the diffraction pattern on a screen that is a distance x from the hole. You measure the radius r of the first dark ring in the diffraction pattern. You make the measurements for four values of x. Your results are given in the table. (a) Use each set of measurements to calculate D. Because the measurements contain some error, calculate the average of the four values of D and take that to be your reported result. (b) For x = 1.00 m, what are the radii of the second and third dark rings in the diffraction pattern?
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