Q.Two independent monochromatic sources cannot act as coherent sources, why?

Two light sources are said to be coherent if the waves they emit maintain the same phase, or a constant phase difference, over time, along with the same frequency (monochromaticity), the same waveform, and preferably the same amplitude -- only coherent sources can produce a stable, stationary interference pattern. Two genuinely independent monochromatic sources (e.g. two separate lamps) can never be mutually coherent, because atoms emit light in short, random bursts due to thermal vibrations, so any phase relationship between two independent sources drifts randomly and averages out, giving incoherent light. Three practical techniques are used instead to derive two coherent beams from a single source: (i) amplitude (or intensity) division, in which a half-silvered mirror (beam splitter) splits one beam into a reflected part and a refracted part that remain in step because they originated from the very same wavefront (used in instruments like the Michelson interferometer and the Fabry-Perot etalon); (ii) wavefront division, in which two different points on the same wavefront from a single point source are isolated (for …