A miniature spectrometer used for chemical analysis has a diffraction grating with 800 slits \(/ \mathrm{mm}\) set \(25.0 \mathrm{~mm}\) in front of the detector "screen." The detector can barely distinguish two bright lines that are \(30 \mu \mathrm{m}\) apart in the first-order spectrum. What is the resolution of the spectrometer at a wavelength of \(600 \mathrm{~nm}\) ? That is, if two distinct wavelengths can barely be distinguished, one of them being \(600.0 \mathrm{~nm}\), what is the wavelength difference \(\Delta \lambda\) between the two?