Conditions for detecting lensed Population III galaxies in blind surveys with the <i>James Webb Space Telescope</i>, the <i>Roman Space Telescope</i>, and <i>Euclid</i>

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