= Solution
The <Lyman-alpha forest> is the large collection of narrow <Lyman-alpha absorption> features in the spectrum of a distant <quasar>. Neutral <hydrogen> in foreground gas absorbs at its own redshifted $1s\to2p$ resonance, so an absorber at $z_{\rm abs}$ places its feature at
$$
\lambda_{\rm obs}=1215.67\,(1+z_{\rm abs})\,\text{Å}.
$$
Ordinary intervening absorbers have $z_{\rm abs}<z_Q$, putting their <Lyman-alpha lines> blueward of the quasar's own broad <Lyman-alpha emission>. Many different absorbing patches along the same <line of sight> make the forest; they are not different transitions of one cloud. At sufficiently short wavelengths higher Lyman-series transitions can overlap the forest, so an actual analysis identifies these blends rather than treating every dip as isolated Ly-alpha.
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2005/iii/paper-74-forest.png]
{title=Schematic quasar Lyman-alpha forest and neutral-hydrogen column-density distribution at redshift three}
The upper panel is an original schematic spectrum for $z_Q=3$, with absorption features at smaller <cosmological redshifts> and a broad emission feature near $4863$ Å. The lower panel anticipates the column-density discussion: both curves are teaching sketches, not measured spectra or fitted survey distributions. The ordinary <Lyman-alpha forest> mainly traces the fluctuating, photoionized <intergalactic medium>, rather than a collection of identical isolated, neutral clouds.
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