Sorry, the resolution that's in the denominator of dλ/dθ is some sort of a dimensionless quantity, which actually is the ratio between the wavelength of interest and the spectral resolution. So essentially something like 4500 angstrom divided by 0.1 angstrom.
I am stuck on a problem regarding the minimum magnitude of an astronomical object that can be handled by a given telescope+spectroscope combination. The telescope aperture (D_T) is 2 m wide, the exit beam (D1) is 3 cm wide. The slit width (s) is 10 micrometers. The wavelength of interest is 450...