  We present new diagnostics of white dwarf (WD) cooling sequences and
luminosity functions (LFs) in the near-infrared (NIR) bands that will exploit
the sensitivity and resolution of future extremely large telescopes. The
collision-induced absorption (CIA) of molecular hydrogen causes a clearly
defined blue turn-off along the WD (WDBTO) cooling sequences and a bright
secondary maximum in the WD LFs. These features are independent of age over a
broad age range and are minimally affected by metal abundance. This means that
the NIR magnitudes of the WDBTO are very promising distance indicators. The
interplay between the cooling time of progressively more massive WDs and the
onset of CIA causes a red turn-off along the WD (WDRTO) cooling sequences and a
well defined faint peak in the WD LFs. These features are very sensitive to the
cluster age, and indeed the K-band magnitude of the faint peak increases by
0.2--0.25 mag/Gyr for ages between 10 and 14 Gyr. On the other hand, the faint
peak in the optical WD LF increases in the same age range by 0.17 (V band) and
0.15 (I band) mag/Gyr. Moreover, we also suggest to use the difference in
magnitude between the main sequence turn-off and either the WDBTO (optical) or
the WDRTO (NIR). This age diagnostic is also independent of distance and
reddening. Once again the sensitivity in the K band (0.15-0.20 mag/Gyr) is on
average a factor of two higher than in the optical bands (0.10 [V band], 0.07
[I band] mag/Gyr). Finally, we also outline the use of the new diagnostics to
constrain the CO phase separation upon crystallization.
