Irina finds an unlabeled box of fine needles, and wants to determine how thick they are. A standard ruler will not do the job, as each needle is less than a millimeter thick. So, to find the thickness, she uses a needle to poke a hole in a piece of brown construction paper. Then, she positions a 657 nm laser pointer to shine through the hole and project a circular diffraction pattern on a wall 22.2 m away. She then uses her ruler to measure that the central bright circle is 12.2 cm in diameter. What diameter does Irina calculate for the needle?