Halliday, Resnick & Walker — Diffraction: Problem 48

48 The wings of tiger beetles (Fig. 36-39) are colored by interference due to thin cuticle-like layers. In addition, these layers are arranged in patches that are $60\ \mu\text{m}$ across and produce different colors. The color you see is a pointillistic mixture of thin-film interference colors that varies with perspective. Approximately what viewing distance from a wing puts you at the limit of resolving the different colored patches according to Rayleigh's criterion? Use $550\ \text{nm}$ as the wavelength of light and $4.50\ \text{mm}$ as the diameter of your pupil.