Chapter 36, Problem 79P

SSM A diffraction grating has resolving power R = λ_avg/Δλ = Nm. (a) Show that the corresponding frequency range ∆ƒ that can just be resolved is given by ∆ƒ = c/Nmλ. (b) From Fig. 36-22, show that the times required for light to travel along the ray at the bottom of the figure and the ray at the top differ by ∆t = (Nd/c) sin θ. (c) Show that (∆ƒ)(∆t) = 1, this relation being independent of the various grating parameters. Assume N ≫1.