$36\mathrm{.}27$ You send coherent $550$ nm light through a diffraction grating that has slits of equal widths and constant separation between adjacent slits. You expect to see the fourth$-$order interference maximum at an angle of with respect to the normal to the grating. However, that order is missing because is also the angle for the third diffraction minimum $($as measured from the central diffraction maximum$)$ for each slit. $($a$)$ Find the center$-$to$-$center distance between adjacent slits. $($b$)$Find the number of slits per mm$.($c$)$ Find the width of each slit.