We measure the galaxy luminosity function ( LF ) for the Virgo Cluster between blue magnitudes M _ { B } = -22 and M _ { B } = -11 from wide-field CCD imaging data .
The LF is only gradually rising for -22 < M _ { B } < -16 .
Between M _ { B } = -16 and M _ { B } = -14 it rises steeply , with a logarithmic slope \alpha \sim - 1.6 .
Fainter than M _ { B } = -14 , the LF flattens again .
This LF is shallower ( although turning up at brighter absolute magnitudes ) than the R -band LF recently measured by Phillipps et al .
( 1998a ) , who found \alpha \sim - 2.2 fainter than M _ { R } = -13 .
It is similar , however , to the LF determined from the Virgo Cluster Catalog by Sandage et al .
( 1985 ) .
A few faint galaxies are found which Sandage et al .
missed because their surface-brightness threshold for detection was too high , but these do not dominate the luminosity function at any magnitude .
Most of the faint galaxies we find are dwarf elliptical , alternatively called dwarf spheroidal , galaxies .
The most important potential source of systematic error is that we may have rejected some high surface-brightness galaxies from the cluster sample because we think that they are background galaxies .
This is quite different from what has conventionally been regarded as the most serious source of systematic error in this kind of study : that we are missing many low surface-brightness galaxies because they are never visible above the sky .

There are about 2.5 times more dwarfs per giant galaxy in Virgo than in the Ursa Major Cluster , a diffuse group of about 80 spiral galaxies at the same distance as Virgo , or the Local Group .
The Virgo and Ursa Major Cluster LFs are inconsistent with each other at a high level of significance .
These results add weight to the hypothesis that is developing that dwarf galaxies are more common relative to giant galaxies in dense environments than diffuse ones .
Both LFs are highly inconsistent with cold dark matter theory , which has been so successful at reproducing observations on large scales .
Possible theoretical explanations for this discrepancy , and for the detailed shape of the Virgo Cluster LF , are investigated .