Problem 5.142

A transparent diffraction grating of a quartz spectrograph is \(25 \mathrm{~mm}\) wide and has 250 lines per millimetre. The focal length of an objective in whose focal plane a photographic plate is located is equal to \(80 \mathrm{~cm}\). Light falls on the grating at right angles. The spectrum under investigation includes a doublet with components of wavelengths 310.154 and 310.184 nm. Determine: (a) the distances on the photographic plate between the components of this doublet in the spectra of the first and the second order; (b) whether these components will be resolved in these orders of the spectrum.