Herring and related fish have a brilliant silvery appearance that camouflages them while they are swimming in a sunlit ocean. The silveriness is due to platelets attached to the surfaces of these fish. Each platelet is made up of several alternating layers of crystalline guanine $(n=1.80)$ and of cytoplasm $(n=1.333$, the same as water), with a guanine layer on the outside in contact with the surrounding water (Fig. $\mathbf{P 3 5 . 4 8}$ ). In one typical platelet, the guanine layers are $74 \mathrm{nm}$ thick and the cytoplasm layers are $100 \mathrm{nm}$ thick. (a) For light striking the platelet surface at normal incidence, for which vacuum wavelengths of visible light will all of the reflections $R_{1}, R_{2}, R_{3}, R_{4},$ and $R_{5}$ shown in Fig. $\mathrm{P} 35.48$, be approximately in phase? If white light is shone on this platelet, what color will be most strongly reflected (see Fig. 32.4 )? The surface of a herring has very many platelets side by side with layers of different thickness, so that all visible wavelengths are reflected. (b) Explain why such a "stack" of layers is more reflective than a single layer of guanine with cytoplasm underneath. (A stack of five guanine layers separated by cytoplasm layers reflects more than $80 \%$ of incident light at the wavelength for which it is "tuned.") (c) The color that is most strongly reflected from a platelet depends on the angle at which it is viewed. Explain why this should be so. (You can see these changes in color by examining a herring from different angles. Most of the platelets on these fish are oriented in the same way, so that they are vertical when the fish is swimming.)