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Double Slit Hoodie

DARK WHERE THE PATHS DISAGREE | Pixelated Physics

\[I(\theta) = I_0\cos^2\!\left(\frac{\pi d\sin\theta}{\lambda}\right)\mathrm{sinc}^2\!\left(\frac{\pi a\sin\theta}{\lambda}\right)\]
$54.99 USD
$54.99 USD
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Size guide S–5XL · inches

Light through two narrow slits does not make two bright lines. It makes stripes. Two-slit interference: cos² fringes under a single-slit sinc² envelope. With slits 4 widths apart, every 4th bright order vanishes. Pixel-art unisex hoodie in black; equation, symbols and sources in the physics panel below.

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Details

Size & fitS–5XL

Unisex Heavy Blend hoodie (Gildan 18500), classic fit.

SizeWidthLengthSleeve
S202733.5
M222834.5
L242935.5
XL263036.5
2XL283137.5
3XL303238.5
4XL323339.5
5XL343440.5

Measurements in inches. Width and length ±1 in, sleeve (from center back) ±0.75 in.

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Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

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The physics

Light from two slits interferes, giving bright stripes wherever the path difference is a whole number of wavelengths. The width of each slit adds a broader diffraction envelope that modulates how bright the stripes are.

Light through two narrow slits does not make two bright lines. It makes stripes.

Where the two paths differ by a whole number of wavelengths the waves add, and where they differ by a half they cancel. That gives the cos² fringes. Each slit also has a width, and diffraction from a single slit lays a sinc² envelope over the whole pattern.

In the art the slits sit four slit-widths apart, d = 4a. Every fourth bright fringe then lands exactly on a zero of the envelope and disappears. The gaps in the barcode are the missing orders.

Thomas Young reported interference fringes to the Royal Society in 1803, splitting a sunbeam with a thin card; the two-slit version appears in his 1807 Lectures. Sent through one photon at a time, the light still builds up the same stripes.

Dark where the paths disagree.

Equations

\[I(\theta) = I_0\cos^2\!\left(\frac{\pi d\sin\theta}{\lambda}\right)\mathrm{sinc}^2\!\left(\frac{\pi a\sin\theta}{\lambda}\right)\]
\[d\sin\theta = m\lambda \;\text{(bright)}\]
\[d = 4a\]
SymbolMeaningUnit
\(I(\theta)\) intensity on the screen at angle \theta \(\mathrm{W/m^2}\)
\(I_0\) intensity at the centre \(\mathrm{W/m^2}\)
\(d\) distance between the slit centres \(\mathrm{m}\)
\(a\) width of each slit \(\mathrm{m}\)
\(\lambda\) wavelength \(\mathrm{m}\)
\(\theta\) angle from the axis \(\mathrm{rad}\)
\(m\) order of a bright fringe \(\mathrm{1}\)
\(\mathrm{sinc}\,x\) \sin x / x \(\mathrm{1}\)

Sources

  1. Young (1804) Experiments and Calculations relative to Physical Optics, Phil. Trans. R. Soc. 94, 1
  2. Hecht, Optics, 5th ed., Ch. 9: Interference and Ch. 10: Diffraction
  3. Feynman Lectures on Physics Vol. III Ch. 1: Quantum Behavior

Source Young, T. (1804). The Bakerian Lecture: Experiments and calculations relative to physical optics. Philosophical Transactions of the Royal Society of London 94, 1–16.doi.org/10.1098/rstl.1804.0001

Field notes

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