Babinet's principle states that, except for differences in intensity, the interference pattern created by light passing around an opaque object is the same as the pattern created by the same light passing through a hole of the same size and shape as the object. You shine a \(690-\mathrm{nm}\) laser beam on a human hair and observe an interference pattern on a screen \(1.2 \mathrm{~m}\) from the hair. If each firstorder dark fringe is \(16 \mathrm{~mm}\) from the center of the pattern, what is the diameter of the hair?