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Optical activity is the ability to rotate the direction of linear polarization of transmitted light. In an achiral solvent, the two members of an enantiomer pair have equal and opposite optical rotations at the same wavelength, temperature and concentration. The measured angle concerns a bulk sample; it is not a geometric rotation of the molecules.^[ref]

The rotating object in this description is the direction along which the electric field oscillates. At each position the transmitted light can still have linear polarization: its electric field moves back and forth along a line, while the orientation of that line changes along the sample. Nothing requires the molecules to turn bodily through the observed angle. This makes polarimetry a bridge from molecular chirality to a visible bulk measurement, and, with a suitable calibration, a way to follow concentration or the balance of enantiomers.

In a transparent, isotropic chemical solution, natural optical rotation can be understood as circular birefringence: the two opposite circular polarizations accumulate different wave phases, and their equal-amplitude sum remains linearly polarized along a rotated direction. Circular dichroism instead means unequal absorption of those components and can produce elliptical polarization. These are related responses, not interchangeable measurements. General birefringence need not produce this simple rotation of linear polarization.^[ref]

For a chemical solution in a validated linear regime,where $l$ is path length in $\mathrm{dm}$ and $c$ is solute mass per final solution volume in $\mathrm{g}\mathrm{m}{\mathrm{L}}^{-1}$. These conventions give specific rotation units $\mathrm{deg}\mathrm{mL}{\mathrm{g}}^{-1}\mathrm{d}{\mathrm{m}}^{-1}$. Specify solvent, temperature $T$ and wavelength $\lambda$: specific rotation is conditional on the sample environment.^[ref]

For an original model, stipulate an unnamed enantiomer pair in the same achiral solvent at $T=20^{\circ }\mathrm{C}$ and wavelength $\lambda =589\mathrm{nm}$. Assign the positive member specific rotation $+40\mathrm{deg}\mathrm{mL}{\mathrm{g}}^{-1}\mathrm{d}{\mathrm{m}}^{-1}$, assumed constant over the modeled concentrations. With $l=1\mathrm{dm}$ and $c=0.200\mathrm{g}\mathrm{m}{\mathrm{L}}^{-1}$,These are chosen model parameters, not measured properties of a named material. Doubling only $l$ or only $c$ doubles $\alpha$ within this stipulated linear model; doubling both multiplies it by four. A real chemical solution must be checked for concentration dependence rather than assuming that $0.200\mathrm{g}\mathrm{m}{\mathrm{L}}^{-1}$ is dilute enough.

For an additive mixture containing only this enantiomer pair as solutes, put $k=[\alpha {]}_{+}$ and write $c_{+},c_{-}$ for their mass concentrations. ThenBecause enantiomers have the same molar mass, their relative mole fractions within the pair also equal their relative mass fractions: $c_{+}=x_{+}c$, $c_{-}=x_{-}c$. Thus $\alpha =klc(x_{+}-x_{-})$, which connects optical rotation to enantiomeric excess.