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Chirality means that a molecule cannot be superposed on its mirror image. A carbon attached to four different groups is a common source of chirality; the definition concerns the whole molecule, rather than requiring this particular structural feature.

The test is spatial: apply a translation and a rotation to the entire molecule until corresponding chemical atoms coincide, keeping their identities and chemical bonds. A mirror operation is a reflection; physically turning a model is a rotation. They are different operations. If no such superposition exists, the two forms are enantiomers; if one succeeds, the molecule is achiral. A different-looking flat drawing alone establishes neither conclusion.

For a simple molecule with exactly one tetrahedral stereocenter and four constitutionally different substituents, the mirror forms cannot superpose. Compare entire attached groups, including paths around a ring, rather than just the first chemical atom. Several tetrahedral stereocenters require a whole-molecule check: a meso compound can be achiral. Conversely, axial chirality needs no tetrahedral stereocenter.^[ref]

Why care about this distinction? Two enantiomers can fit differently into an already chiral molecule, just as two opposite hands fit differently into one glove. Thus a protein's spatial arrangement can distinguish a mirror pair even when an achiral measurement cannot. Polarimetry provides a different kind of test: it measures a sample's net optical rotation, which depends on the populations of its enantiomers.

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]

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.

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 racemate contains the same amount of substance of each member of an enantiomer pair. Their equal and opposite contributions cancel in ordinary solution polarimetry under identical conditions. Zero net optical rotation therefore does not establish achirality of the individual molecules.^[ref]