When assessing a diffraction grating, we are interested not only in its resolving power R, which is the ability of the grating to separate two close wavelengths, but also in the dispersion D of the grating. This is defined by D = Δθm/Δλ in the mth order.

(a) Show that D can be written

Where d is the slit spacing.
(b) If a diffraction grating with 2000 slits per centimeter is to resolve the two yellow sodium lines in the second order (wavelengths 589.0 and 589.6 nm), how many slits must be illuminated by the beam?
(c) What would the separation be between these resolved yellow lines if the pattern were viewed on a screen 4 m from thegrating?

D = Vd? m22