Using the index of refraction, n, with Bragg's Law, λ_p = 2 n_avg d sin(θ), and the relationship between the radius of close-packed spheres and the layer spacing, d =  r = 1.633 r, and θ=90° for the absorbance measurement yields

λ_p = 1.633 D_s [n_s² f + n_v² (1-f)]^1/2

λ_p = 658 nm (the wavelength at peak absorbance)
n_s = 1.49 (the index of refraction for the PMMA spheres)
n_v = 1.00 (the index of refraction for the void air spaces)
f = 0.76 (the filling fraction for a close packed structure)
D_s = 290 nm (the diameter of the close packed spheres)