A laser beam $($$=552$ nm$)$ is put through a beam splitter to give $2$ equal intensity beams traveling parallel to one another. One of these beams is directed through a double slit apparatus, and the other beam through a single slit apparatus. The single slit and the double slits are in the same plane and both display fringe patterns on a screen a distance L$=3\mathrm{.}4$ m away.

a$.$ The slit spacing of the double slit apparatus is $0\mathrm{.}45$ mm$.$ What is the distance from the center of the double slit fringe pattern to the $5$th dark fringe?

b$.$ If the third dark fringe of the single slit pattern is the same distance from the center of the single slit pattern as the result for part $($a$),$ what is the single slit width?

To continue, please enter the result of part b$)$ in mm$.$

Round your answer to $2$ decimal places.