We present a detailed analysis of new photometric and spectroscopic da
ta, both in the optical and in the infrared, of the cool white dwarf L
HS 1126. We show that the peculiar energy distribution of this object,
and especially the large infrared flux deficiency, is the result of t
he collision-induced absorption by molecular hydrogen due to collision
s with helium. The effective temperature and the helium abundance are
determined from a fit to the energy distribution while the surface gra
vity is constrained by the trigonometric parallax measurement. We obta
in T(eff) = 5400 +/- 200 K, log g = 7.85 +/- 0.17, and log N(He)/N(H)
= 0.8 +/- 0.2. The nature of the spectroscopic features observed previ
ously in the infrared and in the optical are rediscussed within the co
ntext of both these new observations and our model atmosphere fit.