Halliday, Resnick & Walker — Diffraction: Problem 38

38 Perhaps to confuse a predator, some tropical gyrinid beetles (whirligig beetles) are colored by optical interference that is due to scales whose alignment forms a diffraction grating (which scatters light instead of transmitting it). When the incident light rays are perpendicular to the grating, the angle between the first-order maxima (on opposite sides of the zeroth-order maximum) is about \(24^{\circ}\) in light with a wavelength of \(550 \text{ nm}\). What is the grating spacing of the beetle?