(Solved): Calculate (a) the effective refractive index and (b) the wavelength diffracted from the close packe ...

Calculate (a) the effective refractive index and (b) the wavelength diffracted from the close packed (111) layers for an inverse f.c.c. opal made from ceria $\left({\mathrm{CeO}}_2\right)$ shells, at when the angle of incidence is $25^{?}$, knowing that the volume fraction of ${\mathrm{CeO}}_2$ is $17.8\%$, the refractive index of bulk ${\mathrm{CeO}}_2$ is 2.4 and the shell (sphere) diameter is $238\mathrm{nm}$. (c) Calculate the first four photonic band gap wavelengths for the inverse opal described.