You Find an unlabeled box of fine needles, and want to determine how thick they
ID: 1501397 • Letter: Y
Question
You Find an unlabeled box of fine needles, and want to determine how thick they are. A standard ruler won't do the job. since all you can tell is that each needle is less than a millimeter thick. So to Find the thickness, you use the needle to poke a hole in a piece of brown construction paper. Then you arrange your 640 nm laser pointer to shine through the hole, and a circular diffraction pattern, consisting of a central bright circle surrounded by alternating dark and bright rings, appears on the wall 22.7 m away. Now you can use your ruler to measure that the central bright circle is 18.2 cm in diameter. What is the diameter of the needle?Explanation / Answer
at the end of first bright fringe, first dark fring starts.
hence position of 1st dark fringe will be radius of central fringe.
r = 0.5 * lambda * D / d
(0.182/2) = (0.5 x 640 x 10^-9 x 22.7) / d
d = 79.8 x 10^-6 m = 79.8 um
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