= Solution
Adjacent <longitudinal cavity modes> obey $2nL=m\lambda_0$. Neglecting <optical dispersion> in estimating their spacing,
$$
\Delta\nu=\frac{c}{2nL}=8.33\times10^{10}\,\mathrm{Hz},\qquad
\Delta\lambda_0\simeq\frac{\lambda_0^2}{2nL}=0.1778\,\mathrm{nm}.
$$
Hence the gain interval accommodates
$$
\boxed{N\simeq\frac{20}{0.1778}=112.5\simeq113}
$$
possible <longitudinal cavity modes>. The exact integer depends on the positions of the interval endpoints and resonances. This counts available resonances; mode competition and actual <laser threshold> can reduce the number that oscillates. More accurately, the spacing uses the <group refractive index> instead of $n$.
A broad multimode spectrum suffers differential delay through <optical fiber> <group velocity dispersion>, broadening transmitted pulses. Near $800\,\mathrm{nm}$, ordinary silica <optical fiber attenuation> is also larger than in the long-distance windows near $1.3$ and $1.55\,\mu\mathrm m$. These limitations concern this short-wavelength, simple multimode device: suitably engineered single-frequency <semiconductor lasers> at telecommunications <wavelengths> are useful communication sources.
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