It depends on the type of instrument. A narrower slot is normally used in a scanning type instrument. Many instruments these days are not scanning.
With the Public lab type instrument, the number of lines in the grating(aka the dvd) is one item that can go a long way to determine resoluntion. But there are a lot of others that also contribute( harmonic filters, distances, etc.). Your best bet is to get some optics books or to talk to someone much more experienced.
Sorry I can't help more.