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 23.2 m away. Now you can use your ruler to measure that the central bright circle is 17.2 cm in diameter. What is the diameter of the needle?
___________um