Procedure by William Schreiter, Richard Amankwah and Karen Nordell, Chemistry Department, Lawrence University.
The maximum absorbance for this close packed film occurs at 658 nm. The index of refraction for PMMA is 1.49 and the index of refraction of air is 1.00. Using the equation here, the calculated diameter of the close-packed spheres is 290 nm.
λp = 1.633 Ds [ns2 f + nv2 (1-f)]1/2
λp = 650 nm (the wavelength at maximum absorbance)
Ds = the diameter of the close packed spheres (in nm)
ns = 1.49 (the index of refraction for the spheres)
nv = 1.00 (the index of refraction for the void spaces)
f = 0.76 (the filling fraction for a close packed structure)