A colloidal crystal is grown from silica spheres across

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Condensed Matter, Materials & Soft Matter · Interference and diffraction

Condensed Matter Physics, Ch Soft matter: when entropy, not bonding, sets the structure

Problem

A colloidal crystal is grown from silica spheres

300\,\mathrm{nm}

across, packed face-centred cubic with an effective refractive index of

1.35

. Find the colour it reflects at normal incidence, building the calculation in three named steps: ((a)) the conventional lattice constant

a

from the touching-sphere condition (Chapter 1's close packing); ((b)) the

(111)

plane spacing

d_{111}

from

a

(Chapter 2's Miller indices); ((c)) the reflected wavelength from Bragg's law (Chapter 3), adjusted for the refractive index inside the crystal.