(a) If a diffraction grating has a resolution of 10⁴, is it possible to distinguish two spectral lines with wavelengths of 10.00 and 10.01 µm?

(b) With a resolution of 10⁴, how close in wavenumbers (cm^-1) is the closest line to 1 000 cm^-1 that can barely be resolved?

(c) Calculate the resolution of a 5.0-cm-long grating ruled at 250 lines/mm for first-order (n = 1) diffraction and tenth-order (n = 10) diffraction.

 (d) Find the angular dispersion (Δϕ in radians and degrees) between light rays with wavenumbers of 1 000 and 1 001 cm^-1 for second-order diffraction (n = 2) from a grating with 250 lines/mm and ϕ = 30°.