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Coherent sources of light

Interference · Physics

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Study notes

(a) Two independent laser pointers shine on the same screen. Will you see stable interference fringes? (b) Sunlight filtered to λ = 550 nm has coherence time ~10⁻⁸ s. What is the coherence length? (c) In a Michelson interferometer with one arm 1 m longer than the other, which source works: the filtered sunlight or a laser with coherence length 10 m? Step 1: No — the two pointers are independent sources with randomly drifting relative phase; any instantaneous fringe pattern shifts ~10⁸ times per second and averages to uniform illumination. Split ONE laser into two beams and fringes appear. Step 2: Coherence length L_c = c × τ_c = 3×10⁸ × 10⁻⁸ = 3 m. Wave trains stay phase-predictable over ~3 metres. Step 3: Path difference = 2 × 1 m = 2 m (round trip). Filtered sunlight (L_c = 3 m) barely works — fringes visible but low contrast near the limit. The laser (10 m) works comfortably. This is exactly why precision interferometry uses lasers: long coherence length tolerates large path differences.

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