## Interpretation

Equation clearly states that the sensitivity to extended sources depends on the dilution of the synthesized beam in the primary beam. This is why this formulation of the sensitivity is well adapted to resolved sources.

For a given interferometer, the primary beamwidth is a fixed quantity while the synthesized beam is to first order proportional to the longest baseline in the current interferometer configuration. Hence, doubling the largest baseline will multiply by a factor for the same integration time or it will multiply the integration time by a factor in order to reach the same sensitivity. This just reflects that while the interferometer tries to mimic a single-dish antenna of same diameter as the largest baseline, all the antenna of the interferometer only fill a fraction of the total collecting area of the single-dish, this fractions decreasing with a power of two as the baseline linearly increases.