  We calculate the optical bj luminosity function of the 2dF Galaxy Redshift
Survey (2dFGRS) for different subsets defined by their spectral properties.
These spectrally selected subsets are defined using a new parameter, eta, which
is a linear combination of the first two projections derived from a Principal
Component Analysis. This parameter eta identifies the average emission and
absorption line strength in the galaxy rest-frame spectrum and hence is a
useful indicator of the present star formation. We use a total of 75,000
galaxies in our calculations, chosen from a sample of high signal-to-noise
ratio, low redshift galaxies observed before January 2001. We find that there
is a systematic steepening of the faint end slope (alpha) as one moves from
passive (alpha = -0.54) to active (alpha = -1.50) star-forming galaxies, and
that there is also a corresponding faintening of the rest-frame characteristic
magnitude M* - 5\log_10(h) (from -19.6 to -19.2). We also show that the
Schechter function provides a poor fit to the quiescent (Type 1) LF for very
faint galaxies (M - 5log_10(h) fainter than -16.0), perhaps suggesting the
presence of a significant dwarf population. The luminosity functions presented
here give a precise confirmation of the trends seen previously in a much
smaller preliminary 2dFGRS sample, and in other surveys. We also present a new
procedure for determining self-consistent K-corrections and investigate
possible fibre-aperture biases.
