If sunlight shines straight onto a peacock feather, the feather appears bright blue when viewed from \(15^{\circ}\) on either side of the incident beam of sunlight. The blue color is due to diffraction from the melanin bands in the feather barbules, as was shown in the photograph on page 549 . Blue light with a wavelength of \(470 \mathrm{~nm}\) is diffracted at \(15^{\circ}\) by these bands (this is the firstorder diffraction) while other wavelengths in the sunlight are diffracted at different angles. What is the spacing of the melanin bands in the feather?