Problem 5.141

With light falling normally on a transparent diffraction grating \(10 \mathrm{~mm}\) wide, it was found that the components of the yellow line of sodium \((589.0\) and \(589.6 \mathrm{nm})\) are resolved beginning with the fifth order of the spectrum. Evaluate: (a) the period of this grating; (b) what must be the width of the grating with the same period for a doublet \(\lambda=460.0 \mathrm{nm}\) whose components differ by \(0.13 \mathrm{nm}\) to be resolved in the third order of the spectrum.