• Pixel-art sticker of Gratix, personifying Diffraction Grating, with the caption “Many Slits, Sharp Colours.”

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Gratix

Diffraction Grating Physics

\[d\sin\theta = m\lambda\]
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Flat $6 shipping worldwideMade to order, ships in 2–5 business days

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Size3″ × 3″

3″ × 3″ kiss-cut sticker.

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Flat $6 shipping on every order, worldwide, whatever's in it.

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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

Meet Gratix, a diffraction grating who splits light into sharp beams of colour.

A grating has many equally spaced slits or lines. Light through neighbouring slits travels different distances, and where the extra distance is a whole number of wavelengths the waves add up brightly. This happens at angles where d sin θ = mλ.

A grating with 600 lines per millimetre has spacing d = 1 / 600 mm ≈ 1.67 µm. For green laser light of 532 nm, the first-order beam (m = 1) is at sin θ = 0.532 / 1.67 ≈ 0.32, so θ ≈ 18.6°. Red light, with a longer wavelength, bends further.

With thousands of slits, the bright beams become very narrow, much sharper than with two slits. That is why gratings can separate wavelengths that are very close together, which a prism cannot do as well.

Gratings are at the heart of spectrometers, which reveal the elements in stars and the chemicals in a lab sample. The rainbow sheen on a CD comes from its closely spaced tracks, which act as a reflection grating.

Equations

\[d\sin\theta = m\lambda\]
Symbols
SymbolMeaningUnit
\(d\) spacing between neighbouring slits \(\mathrm{m}\)
\(\theta\) angle of a bright beam from the straight-through direction \(\mathrm{rad}\)
\(m\) order of the bright beam (an integer) —
\(\lambda\) wavelength of the light \(\mathrm{m}\)