Q$9$: Two rectangular, optically flat glass plates $($index of refraction $1\mathrm{.}63)$ are in contact along one end and are separated along the other end by a spacer that is $4\mathrm{.}8\backslash$mu m thick. The top plate is illuminated by monochromatic light of wavelength $560\mathrm{.}6$ nm$.$ Calculate the number of dark parallel bands crossing the top plate $($including the dark band at zero thickness along the line of contact between the two plates$).$ The last dark band is to be counted if and only if its center $($where the intensity is zero$)$ is present. Answer in units of dark fringes.