  The width $\triangle_L$ of the first Bragg's scattering peak in the (111)
direction of a face-centered-cubic lattice of air spheres can be well
approximated by a simple formula which only involves the volume averaged
$\epsilon$ and $\epsilon^2$ over the lattice unit cell, $\epsilon$ being the
(position dependent) dielectric constant of the medium, and the effective
dielectric constant $\epsilon_{eff}$ in the long-wavelength limit approximated
by Maxwell-Garnett's formula. Apparently, our formula describes the asymptotic
behaviour of the absolute gap width $\triangle_L$ for high dielectric contrast
$\delta$ exactly. The standard deviation $\sigma$ steadily decreases well below
1% as $\delta$ increases. For example $\sigma< 0.1%$ for the sphere filling
fraction $f=0.2$ and $\delta\geq 20$. On the interval $\delta\in(1,100)$, our
formula still approximates the absolute gap width $\triangle_L$ (the relative
gap width $\triangle_L^r$) with a reasonable precision, namely with a standard
deviation 3% (4.2%) for low filling fractions up to 6.5% (8%) for the
close-packed case. Differences between the case of air spheres in a dielectric
and dielectric spheres in air are briefly discussed.
