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.