Physics · Ch 6 — Optics
Coherent Sources
Coherent Sources
Two light sources are coherent if they produce waves of the same phase or constant phase difference, the same frequency (monochromatic), the same waveform, and preferably the same amplitude -- coherence is exactly the property that lets a stable, stationary interference pattern be observed. Two genuinely independent monochromatic sources can never be mutually coherent, because atoms emitting light undergo random phase changes due to thermal vibrations, so any relationship between two independent sources' phases is random and averages away; such sources are called incoherent. Three techniques instead derive two coherent beams from a single source: (i) intensity (amplitude) division -- passing light through a partially silvered mirror (beam splitter) simultaneously reflects and refracts it, giving two beams that stay in phase (or at constant phase difference) since they came from the same original wavefront, the principle behind instruments like Michelson's interferometer and the Fabry-Perot etalon; (ii) wavefront division -- since every point of a single wavefront is already in phase, using a double slit to isolate two points on the same wavefront gives two coherent sources, the most commonly used method; and (iii) source and images -- a source together with its own real or virtual image (from a mirror or biprism) forms a coherent pair, since the image's w …
What this figure shows. Light from a single monochromatic source strikes a half-silvered (partially reflecting) mirror acting as a beam splitter, splitting into two separate beams -- one reflected, one transmitted through and then reflected off a second full mirror -- which are then brought back together. Because both beams originated from literally the same wavefront of the same source, they remain coherent (in phase or at a fixed phase difference) however far apart their two paths take them before recombining; this amplitude-division technique is the operating princ …
What this figure shows. A single point source S produces an outward-spreading spherical wavefront; a double slit placed in the path of this wavefront isolates two nearby points on it, S1 and S2, both automatically in phase with each other since they both sit on the same original wavefront at the same instant. These two illuminated slit-points now act as a pair of coherent secondary sources -- this wavefront-division technique is the one used in Young's double-slit experiment, the most commo …
What this figure shows. Two named experimental arrangements are shown side by side. Fresnel's biprism uses a single real source together with a thin double-angled prism to produce two overlapping virtual images of that one source, which then act as a coherent source pair, with interference fringes visible in the overlapping (superposition) region beyond. Lloyd's mirror instead uses a single real source held close to the plane of a mirror, whose reflection produces one virtual image; the original real source and its own virtual image together form the coherent pair, again producing an overlapping superposition …