--- title: "Coherence and Young's Double-Slit Fringes" description: "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 " canonical: https://lightmysky.com/learn/science/coherence-and-youngs-double-slit-fringes-mt_mONvXhPmwq source: https://lightmysky.com/learn/science/coherence-and-youngs-double-slit-fringes-mt_mONvXhPmwq.md retrieved: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # 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. Subject: Science · Area: Waves, Light & Sound · Ages 16 to 18 Page: https://lightmysky.com/learn/science/coherence-and-youngs-double-slit-fringes-mt_mONvXhPmwq ## Ready when they can - 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 ## Lesson: Two slits that paint with light 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. *(drawing: Dots mark example fringe centres with 2 mm spacing. This is a position scale, not an intensity curve or a ray diagram.)* 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. **Example.** 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. 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. **Recap.** 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.* ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Superposition and Stationary Waves](https://lightmysky.com/learn/science/superposition-and-stationary-waves-mt_AIxA2TYGJN) ## Opens up - [Phasor Addition and the Mathematics of Interference](https://lightmysky.com/learn/science/phasor-addition-and-the-mathematics-of-interference-mt_dxh7HHbIUw) - [Single-Slit Diffraction and the Limit of Resolution](https://lightmysky.com/learn/science/single-slit-diffraction-and-the-limit-of-resolution-mt_qiG0fGadBU) - [The Michelson Interferometer](https://lightmysky.com/learn/science/the-michelson-interferometer-mt_Wlb1tZnJBi) - [The Diffraction Grating and Measuring Wavelength](https://lightmysky.com/learn/science/the-diffraction-grating-and-measuring-wavelength-mt_yIjB-uJuFt)