= Specific rotation
{title2=$[\alpha]_{\lambda}^{T}$}
For a dilute <chemical solution> in the usual linear regime,
$$
\alpha=[\alpha]_{\lambda}^{T}\,l\,c,
$$
where $l$ is path length in $\mathrm{dm}$ and $c$ is mass <concentration> in $\mathrm{g\,mL^{-1}}$. These conventions give <specific rotation> units $\mathrm{deg\,dm^{-1}\,mL\,g^{-1}}$. Specify <solvent> as well as <temperature> $T$ and <wavelength> $\lambda$. <Specific rotation> is conditional on these settings, not a universal number independent of the sample environment.<Organic Chemistry by John McMurry/5.3 Optical Activity>[McMurry, Organic Chemistry, §5.3: observed rotation divided by path length and mass concentration]{ref}
For an ideal additive mixture of just two <enantiomers>, write $k$ for the <specific rotation> of the positive member under the chosen conditions and $c_+,c_-$ for their mass <concentrations>. Then $\alpha=kl(c_+-c_-)$, while total mass <concentration> is $c_++c_-$. Equal populations give zero without either member losing its <chirality (chemistry)>. A small signal can also mean low <concentration> or weak <optical rotation> at the selected <wavelength>; other sample components can cancel or alter the signal. Inferring composition from $\alpha$ requires a validated mixture model and a reference measured under matching conditions.
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