  Dark matter halos that reach the HI-cooling mass without prior star formation
or external metal pollution represent potential sites for the formation of
small - extremely faint - Population III galaxies at high redshifts.
Gravitational lensing may in rare cases boost their fluxes to detectable
levels, but to find even a small number of such objects in randomly selected
regions of the sky requires very large areas to be surveyed. Because of this, a
small, wide-field telescope can in principle offer better detection prospects
than a large telescope with a smaller field of view. Here, we derive the
minimum comoving number density required to allow gravitational lensing to lift
such objects at redshift $z=5-16$ above the detection thresholds of blind
surveys carried out with the James Webb space telescope (JWST), the Roman space
telescope (RST) and Euclid. We find that the prospects for photometric
detections of Pop III galaxies is promising, and that they are better for RST
than for JWST and Euclid. However, the Pop III galaxies favoured by current
simulations have number densities too low to allow spectroscopic detections
based on the strength of the HeII1640 emission line in any of the considered
surveys unless very high star formation efficiencies ($\epsilon > 0.1$) are
envoked. We argue that targeting individual cluster lenses instead of the wide
field surveys considered in this paper results in better spectroscopic
detection prospects, while for photometric detection, the wide field surveys
perform considerably better.
