How do you see something smaller than light can resolve — the atoms in a crystal? You bounce X-rays off it. At most angles the reflections cancel to nothing; but at a few special angles the waves from each layer line up perfectly and flash bright. Those flashes are a map of the atoms. Slide the angle and catch the peaks.
X-rays reflecting off successive atomic planes (spacing d) travel an extra distance 2d·sinθ. They interfere CONSTRUCTIVELY — a bright diffraction spot — only when that path difference is a whole number of wavelengths: nλ = 2d·sinθ (Bragg’s law, 1913). Sweep the angle and the detector is dark except at the sharp Bragg angles, whose pattern reveals the atomic spacing. A fail-loud self-check throws unless a bright peak occurs exactly where 2d·sinθ equals an integer number of wavelengths.
A single set of parallel planes and a monochromatic beam here; real crystals have many plane families (giving many spots) and the structure factor modulates intensities. Bragg’s law itself is exact.