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 670 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 22.2 m away. Now you can use your ruler to measure that the central bright circle is 13.2 cm in diameter. What is the diameter of the needle?

I followed the previous steps as similar example posted on chegg however the answer turned out to be wrong in my similar problem. I could not identify what I did wrong.

The incorrect answers I inputed were as follows:112.68, 225, 1.12, 137.

I would greatly appriciate your help!

Explanation / Answer

Rayleigh's criteria for resolution for a circular aperature is
theta = 1.22 y / D     where y is the wavelength and D diameter of aperature
theta = 1.22 * 6.7 * 10E-7 / .132 = 6.19 * 10E-6
Now assume that the image was formed (from 2 aperatures) with the center
of 1 image falling on the edge of the other image (just resolved)
Then d (diameter) = S * theta = 22.2 * 6.19 * 10E-6 = 1.37 * 10E-4 m
or 137 um

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