Coherence and Young's Double-Slit Fringes
Coherent waves have the same frequency and a fixed phase difference. For initially in-phase, matching-polarisation slit outputs, whole-wavelength path differences give constructive interference. Near the centre of a distant screen, fringe spacing is approximately w = lambda D/s.
What a learner can do afterwards
- Defines coherence and explains how suitable common-source illumination gives the two slits a stable phase relationship
- Uses the fringe spacing equation to get a wavelength from measurements on a screen
- Predicts what happens to the pattern when the slit separation, the screen distance or the colour changes
1 · Read
Coherent waves have the same frequency and a fixed phase difference over the observation time; they need not be in phase. A suitably prepared common wave can illuminate both slits coherently. Ordinary independent bulbs do not maintain this phase link. Interference needs overlapping field components: nonorthogonal linear polarisations can interfere. Matching polarisations maximise visibility for fixed amplitudes.
Here the slit outputs start in phase, have the same frequency and matching polarisation, and acquire no extra phase shifts. A path difference of m wavelengths gives constructive interference, where m is an integer. An odd half-wavelength difference gives destructive interference. Complete darkness also requires equal arriving amplitudes. Light spreads from each narrow slit, allowing the outputs to overlap.
Near the centre of a distant screen, neighbouring interference fringes are approximately equally spaced: w = lambda D/s. Here w is fringe spacing, lambda is wavelength, D is slit-to-screen distance and s is centre-to-centre slit separation. Use consistent length units. This uses a far-screen geometry and small angles; it is not an exact spacing rule across every angle.
With wavelength and screen distance fixed, w is inversely proportional to slit separation s. Doubling s halves w. Increasing s by a factor of three divides w by three. These predictions assume the same small-angle conditions and enough overlap to observe the fringes.
Rearrange w = lambda D/s to lambda = ws/D. Convert all lengths to metres before substituting. For w = 0.0016 m, s = 0.0006 m and D = 2 m, lambda = 0.0016 × 0.0006 / 2 = 0.00000048 m, or 480 nm. Nanometres convert to metres by multiplying by 10 to the power −9.
The cells show the wavelength calculation, not the slit geometry. The result is 480 nm.
With the geometry fixed, fringe spacing grows with wavelength. Red light has a longer wavelength than blue light in the same medium, so replacing red with blue reduces the spacing. With wavelength and slit separation fixed, increasing the screen distance D increases w by the same factor.
For two ordinary independent bulbs, the relative phase changes rapidly. Their bright and dark interference contributions average out, so no stable fringe pattern remains in a steady measurement. Suitable coherent illumination supplies the stable phase relationship needed here. A common source must also be arranged so both slits receive a sufficiently coherent wave.
Stable fringes need coherence and interfering field components. Matching polarisation is this lesson's assumption. Near a distant screen's centre, w = lambda D/s.
Original lesson, questions and flashcards by the dataset authors.
The rewritten readings were written for this dataset. Videos credited to Khan Academy.
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