Q.What is meant by coherent sources? What are the two methods for obtaining coherent sources in the laboratory?

[!TLDR] Coherent sources emit the same frequency with a constant (not necessarily zero) phase difference; since independent sources can't reliably satisfy this, the two lab methods -- Lloyd's mirror and the Fresnel biprism -- both derive two virtual sources from one single real source instead. [!ANSWER] Coherent sources: same frequency, constant phase difference. L …

Two sources are called COHERENT if they emit waves of the SAME frequency, with a phase difference between them that remains CONSTANT in time -- not necessarily zero, simply unchanging. This is the essential condition for a sustained, visible interference pattern: if the phase relationship instead drifts randomly (as it does for any two genuinely independent primary sources, since each source's emission process is an unrelated physical event), the resulting pattern's bright and dark positions shift continuously, faster than any detector can register, and no stable pattern is ever actually observed -- only an averaged-out uniform intensity. Because two independent sources can never be reliably coherent, the standard practical strategy is always to derive TWO SECONDARY sources from a SINGLE original PRIMARY source, since both secondary sources then automatically stay locked to whatever phase the one original source happens to have at any given instant, regardless of how that source's own phase might itself fluctuate.

Beyond Young's original two slits, two further classic laboratory devices achieve this same single-source-to-two-coherent-sources strategy by DIVISION OF WAVEFRONT:

(i) LLOYD'S MIRROR: light from a source S is directed at a plane mirror held nearly edge-on, so the light strikes the mirror at GRAZING incidence (very close to 90° from the normal). Some light travels directly to a screen; other light reflects off the mirror and, by the ordinary rule for plane-mirror images, appears to originate from a VIRTUAL image source S' located behind the mirror. Since both the real source S and its own virtual image S' trace back to the one single original source S, they form a genuinely coherent pair, and an interference pattern -- mathematically identical in form to Young's double-slit pattern, with S and S' playing the roles of $S_1$ and $S_2$ -- is produced where the direct and reflected beams overlap. …

State the defining condition for coherence (same frequency, constant phase difference) and explain why it forces the single-source-to-two-secondary-sources strategy, then describe Lloyd's mirror (grazing reflection producing a virtual image source) and the Fresnel bip …

Defining coherent sources as requiring EXACTLY zero phase difference, rather than correctly stating the requirement is merely a CONST …