You find an unlabeled box of fine needles, and want to determine how thick they

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 25.2 m away. Now you can use your ruler to measure that the central bright circle is 19.2 cm in diameter. What is the diameter of the needle? answer in micrometers The incorrect answer is1.7886x10*6 and -6

Explanation / Answer

1.22 * wavelength = D y / L where y is the radius of the brigt circle and D is the diam of the needle

1.22 * 640 x 10^-9 = D * 9.6 / 2520

D = 205 um

Not sure what to tell you here... the answer is 205 um. It's a simple diffraction problem, so it's not like there's any other way to do it. If someone is telling you the answer is NOT 205 um, they are making a mistake. If it's an online homework system... they make mistakes also. I know this doesnt help much.

The most likely mistake is that they might be using the diameter of the bright circle instead of the radius. If they did, the answer they would get would be 102.5 um (i.e. half of the correct answer.) If they tell you this answer is correct, then at least you know what mistake they're making. Otherwise... no idea. If you can tell me which book you're using, and if you're using Webassign, I can look up the formula they're using to calculate it and see where the mistake is. I only have access to Webassign, though. Send me a private message, if you want to.

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