A transmission grating having $200$ lines$/$mm is perpendicularly placed in front of a collimated beam. The source generates wavelengths $532\mathrm{.}005$nm and $531\mathrm{.}995$nm$.($a$)$ In order to resolve these two lines from each other, what must be the minimum resolution power for the $1$st order lines in this grating? $($b$)$ Find the length of the grating if the grating is totally illuminated. $($c$)$ If the slit widths are negligibly small, what is the angle of separation of these lines in the first order maximums? $($d$)$ What is the maximum order of interference in this grating? $($e$)$ Can we resolve the $1064\mathrm{.}005$nm and $1063\mathrm{.}995$nm with our grating which is found in part $($b$)?$ IF YES, in which order?