Question: You are designing a diffraction grating that will disperse white light into its spectrum ((400-mathrm{nm}) violet to (700-mathrm{nm}) red). In the first-order spectrum, you want

You are designing a diffraction grating that will disperse white light into its spectrum $(400-\mathrm{nm}$ violet to $700-\mathrm{nm}$ red). In the first-order spectrum, you want the angular separation between the shortest and longest wavelengths to be $12.0^{\circ}$.

(a) How many slits per millimeter should the grating have?

(b) How many complete full-color spectra will the grating produce, not counting the central bright fringe?

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