A pair of parallel slits separated by $1\mathrm{.}70104$ m is illuminated by $583$ nm light and an interference pattern is observed on a screen $3\mathrm{.}00$ mfrom the plane of the slits. Calculate the difference in path lengths from each of the slits to the location on the screen of a fifth$-$order bright fringe and a fifth dark fringe. $($Enter your answers in m$.)$

HINT

$($a$)$

a fifth$-$order bright fringe

m

$($b$)$

a fifth dark fringe

m