  One of the most direct routes for investigating the geometry of the Universe
is provided by the numbers of strongly magnified gravitationally lensed
galaxies as compared with those that are either weakly magnified or
de-magnified. In the submillimetre waveband the relative abundance of strongly
lensed galaxies is expected to be larger as compared with the optical or radio
wavebands, both in the field and in clusters of galaxies. The predicted numbers
depend on the properties of the population of faint galaxies in the
submillimetre waveband, which was formerly very uncertain; however, recent
observations of lensing clusters have reduced this uncertainty significantly
and confirm that a large sample of galaxy-galaxy lenses could be detected and
investigated using forthcoming facilities, including the FIRST and Planck
Surveyor space missions and a large ground-based millimetre/submillimetre-wave
interferometer array (MIA). We discuss how this sample could be used to impose
limits to the values of cosmological parameters and the total density and form
of evolution of the mass distribution of bound structures, even in the absence
of detailed lens modeling for individual members of the sample. The effects of
different world models on the form of the magnification bias expected in
sensitive submillimetre-wave observations of clusters are also discussed,
because an MIA could resolve and investigate images in clusters in detail.
