Specific rotation ($[\alpha {]}_{\lambda }^T$)

For a dilute chemical solution in the usual linear regime,where $l$ is path length in $\mathrm{dm}$ and $c$ is mass concentration in $\mathrm{g}\mathrm{m}{\mathrm{L}}^{-1}$. These conventions give specific rotation units $\mathrm{deg}\mathrm{d}{\mathrm{m}}^{-1}\mathrm{mL}{\mathrm{g}}^{-1}$. 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.^[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. 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.