Optical activity

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]

Optical rotation is the signed angle measured in polarimetry. Positive rotation is clockwise for an observer facing the incoming light; negative rotation is counterclockwise. State the viewing convention, wavelength, temperature, solvent, concentration and path length when comparing measurements. R and S configuration specifies spatial arrangement, and does not predict the sign of optical rotation.^[ref]

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.

Polarimetry measures optical rotation with a polarimeter. A concrete modern experiment uses the vertical Vernier Go Direct instrument: a $589\mathrm{nm}$ light source, fixed polarizer, sample cell, motor-driven analyzer, photodetector and optical rotary encoder. Its readout is transmitted illumination versus analyzer angle. Calibrate with the same solvent filled to $10\mathrm{cm}$, then rinse with sample and fill to $10.0\mathrm{cm}$, reading the bottom of the meniscus to $0.1\mathrm{cm}$. The shifted maximum nearest zero gives $\alpha$; a fit with the square of a cosine uses the whole trace.^[ref]

In an ideal optical model, Malus's law gives $I(\theta )=I_{\max }{\cos }^2(\theta -\alpha )$ after solvent zeroing. Maxima repeat every $180^{\circ }$, so tracking the same peak matters. As an illustrative calculation, not a reported measurement, a peak shift from $0^{\circ }$ to $+5^{\circ }$ at $l=1.00\mathrm{dm}$ and $c=0.100\mathrm{g}\mathrm{m}{\mathrm{L}}^{-1}$ gives $[\alpha ]=+50\mathrm{deg}\mathrm{d}{\mathrm{m}}^{-1}\mathrm{mL}{\mathrm{g}}^{-1}$. This calculation says nothing about R and S configuration.

The solvent blank controls the baseline. A reference sample and a repeat blank can check scale and drift; record temperature, concentration and fill height. Use a transparent homogeneous chemical solution, and remove bubbles and particles. The manual distinguishes $\pm 0.1^{\circ }$ fit reproducibility from its $\pm 1^{\circ }$ accuracy specification, and warns that a failed fit can give an unreasonable angle. A precise-looking fit therefore need not be accurate.^[ref] Neither a zero reading nor a matching specific rotation uniquely identifies a molecule; polarimetry must be interpreted with the sample composition and these controls.

A polarimeter uses polarizers to compare the direction of linear polarization before and after light passes through a sample; polarimetry explains the apparatus, readout and controls.