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    Christiaan Huygens Sticker

    Every Point A Source | Physics

    \[r = v\,\Delta t\]
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    $4.99 USD
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    How does a wave move forward? Christiaan Huygens treated every point on a wavefront as the source of a small new wave. The surface touching all those wavelets is the new wavefront. In his 1690 Traité de la Lumière he used it to explain reflection and refraction; Fresnel later added interference. A 3" pixel-art physicist sticker; equation, symbols and sources in the physics panel below.

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    Size3″ × 3″

    3″ × 3″ kiss-cut sticker.

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    The physics

    Huygens' principle treats every point on a wavefront as a source of small spherical wavelets. After a short time, the new wavefront is the surface that touches all of those wavelets, which explains reflection and refraction.

    Christiaan Huygens treated every point on a wavefront as the source of a small new wave, a wavelet.

    After a time Δt each wavelet has radius r = vΔt. The surface that touches all of them, their envelope, is the new wavefront.

    On the sticker Huygens, in a 1680s periwig and lace jabot, points at an amber row of sources, each sending out a cyan wavelet; the cream bar is the new front they build together.

    He used the idea in his Traité de la Lumière (1690) to explain reflection and refraction. Fresnel later added interference and turned it into diffraction theory.

    Every point a source.

    Equations

    \[r = v\,\Delta t\]
    \[\text{new front} = \text{envelope of the wavelets}\]
    SymbolMeaningUnit
    \(r\) radius of each secondary wavelet after time \Delta t \(\mathrm{m}\)
    \(v\) wave speed in the medium \(\mathrm{m/s}\)
    \(\Delta t\) time step \(\mathrm{s}\)

    Sources

    1. Huygens, C. (1690) Traité de la Lumière, Leiden
    2. Hecht, E., Optics, 5th ed., Ch. 4 (Huygens’ principle)
    3. Wikipedia, Huygens–Fresnel principle

    Source Huygens, C. (1690). Traité de la Lumière. Leiden: Pierre van der Aa.

    Field notes

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