An astronomer wishes to determine the relative heights of the intensity peaks for the bright fringes produced by two wavelengths of radiation emitted by sodium atoms. The wavelengths are \(589.0 \mathrm{~nm}\) and \(589.6 \mathrm{~nm}\), and she uses a diffraction grating with 500.0 slits/mm to disperse the light collected by her telescope.

(a) In which order are the intensity maxima for these two wavelengths farthest apart from each other: \(m=0, m=1\), or \(m=2\) ?

(b) If the part of the diffraction grating covered by the light is \(4.000 \mathrm{~mm}\) wide, are the second-order principal maxima produced by these two spectral lines distinguishable from each other?