Bragg's law
Lawrence Bragg presents his crystal-diffraction relation
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Original prompt & settings (JSON) ↗He was 22, and the relation he presented appeared as nλ = 2d cos θ — not today's sine form, because he measured the angle from the plane normal.
11 November 1912: read to the Cambridge Philosophical Society
William Lawrence Bragg, a 22-year-old Cambridge research student, read “The Diffraction of Short Electromagnetic Waves by a Crystal” to the Cambridge Philosophical Society on 11 November 1912. The published paper identifies J. J. Thomson as the scholar who communicated it to the society.
Bragg reinterpreted the spots from the earlier Munich X-ray experiment as interference among X-rays reflected from successive planes in a crystal. The relation this produced is the one later called Bragg's law.
A cosine, not a sine
The 1912 presentation printed the condition as nλ = 2d cos θ, with θ measured from the plane normal. The modern convention writes nλ = 2d sin θ with θ measured from the plane itself — the discrepancy is one of angle convention.
The paper was not a free-standing equation either. Bragg used the observed pattern to analyze the face-centered structure of zinc sulfide.
The suggestion from the floor
In the discussion after the talk, C. T. R. Wilson suggested testing a strongly cleaving material such as mica. Bragg followed it up and demonstrated specular X-ray reflection from mica.
He sent that result to Nature on 8 December; the talk itself had been abstracted in Nature on 5 December. The full paper appeared in the 1913 Proceedings of the Cambridge Philosophical Society, volume 17, pages 43–57.
Sources
Researched 23 Aug 2026 7 sources 2 audit passes
How this was checked
Researched from the web into a fact sheet, rewritten from that sheet, then audited against it by a different model. How the pipeline works →
What the sources leave uncertain
- The November 11 date is the date the paper was read, not its publication date. The full paper appeared in the 1913 Proceedings.
- The apparent cosine-versus-sine discrepancy is only an angle convention: Bragg’s 1912 angle was measured from the plane normal, while modern θ is measured from the plane.
- Calling this the single creation date of X-ray crystallography is interpretive. Laue, Friedrich and Knipping had already demonstrated X-ray diffraction by crystals earlier in 1912.
Checked against
- The Diffraction of Short Electromagnetic Waves by a Crystal — original paper scan
- The Bragg Law — University of Leeds Special Collections
- Disputed discovery: the beginnings of X-ray diffraction in crystals in 1912
- Bragg’s law — IUCr Online Dictionary of Crystallography
- Lawrence Bragg — Nobel Prize facts
- William Lawrence Bragg — Nobel nomination archive
- 1962 Nobel Prize in Physiology or Medicine