= Solution
Consider a <colloidal photonic crystal> assembled from nearly monodisperse dielectric spheres. Spherical geometry and approximately isotropic interactions favour close-packed arrays, although fcc, hcp and stacking-disordered structures can compete. Sphere diameter $D$ sets the periodic optical length scale. For an ideal close-packed fcc array,
$$
d_{111}=\sqrt{\frac23}D,\qquad\lambda_{\rm Bragg}\simeq2n_{\rm eff}d_{111}
$$
at normal incidence in the simple effective-index picture. Thus changing the building-block size tunes the reflected wavelength; refractive-index contrast affects stop-band strength. Surface charge and screening control colloidal stability and rearrangement during assembly, while polydispersity, roughness and stacking defects broaden the optical response and increase scattering.
\Image[/past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2017/paper-2-photonic-assembly.png]
{title=Building-block size and refractive index set the optical response of a colloidal array}
{source=paper-2-photonic-assembly.py}
This connects sphere-level geometry and material response to collective periodic optical behaviour. The Bragg reflection estimate does not establish a complete three-dimensional photonic band gap.
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