Coherence LengthHardQuestion 20239
Question
A sodium lamp emits two closely spaced wavelengths 589.0 nm and 589.6 nm. They produce interference fringes that disappear and reappear. Fringes disappear (minima of visibility) when:
- AAll fringes overlap completely
- BBright fringes of one wavelength coincide with dark fringes of the otherCorrect
- CPath difference equals coherence length
- DIntensity is zero everywhere
Correct answer
Bright fringes of one wavelength coincide with dark fringes of the other
Explanation
When n₁λ₁ = (n₁ + ½)λ₂, bright fringe of λ₁ overlaps dark fringe of λ₂ → fringes disappear (minimum visibility). This occurs at path difference Δ = λ₁λ₂/(2|λ₁−λ₂|) ≈ λ̄²/(2Δλ). This phenomenon is used to measure wavelength separation (coherence length measurement).