= Relative X-ray wavelength calibration
{title2=$\lambda_1/\lambda_2=n_2\sin\theta_1/(n_1\sin\theta_2)$}
For two lines measured with the same <interplanar spacing> at the same <temperature>, division of <Bragg's law> gives
$$
\frac{\lambda_1}{\lambda_2}
=\frac{n_2\sin\theta_1}{n_1\sin\theta_2}.
$$
The common $d$ cancels. Consequently a precise <wavelength> ratio can coexist with an uncertain conversion to <SI> <length>. In contrast, angular calibration errors generally survive: a shared small zero offset $\epsilon$ changes the inferred ratio fractionally by approximately $(\cot\theta_1-\cot\theta_2)\epsilon$. Nearby lines partially cancel this effect, but widely separated angles need not. Different <crystals>, <temperatures> or <refraction> corrections also prevent unqualified cancellation.
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