Coherent Sources
Two synchronized sources — interference field with hyperbolic bright fringes.
Key Notes
Coherent sources have a constant phase difference and the same frequency — necessary for stable, observable interference.
Two independent ordinary light sources (e.g., two bulbs) are NOT coherent — their phase relationship fluctuates randomly on ~ns timescales, averaging the interference pattern to zero.
In practice, coherent sources are obtained from a single source by either: (a) division of wavefront (e.g., Young's slits, Fresnel's biprism) or (b) division of amplitude (e.g., thin films, Michelson interferometer).
Coherence length L_c = c·τ_c, where τ_c is the coherence time. For a laser, L_c can be metres; for sunlight ~µm.
When coherent sources superpose: I = I₁ + I₂ + 2√(I₁I₂) cos δ. For incoherent sources, the cosine term averages to zero: I = I₁ + I₂.
Lasers are highly coherent (both temporal and spatial). Sunlight has low temporal coherence — that's why thin-film colors require very thin films (within coherence length).
Formulas
Phase difference (coherent)
Defining property of coherent sources.
Total intensity
Standard interference superposition for two coherent sources.
Incoherent sum
Cosine term averages to zero for incoherent sources.
Coherence length
Distance over which the light maintains a stable phase relationship.
Imax / Imin (equal I)
When two equal-intensity coherent sources superpose.
Important Points
Two coherent sources need not have the same amplitude — but they must have a fixed phase relation and the same frequency.
Path difference Δ relates to phase difference: δ = (2π/λ)Δ. Useful for converting between geometric and phase descriptions.
Visibility (fringe contrast) V = (I_max − I_min)/(I_max + I_min). V = 1 only when I₁ = I₂ and coherence is perfect.
Spatial coherence — uniform phase across the wavefront. Temporal coherence — phase stability over time. YDSE needs spatial coherence between the two slits.
A sodium lamp gives sodium-D doublet (589.0 and 589.6 nm) — poor temporal coherence at long path differences.
Coherent Sources notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.