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A physicist associated with optical rotation and Biot's saccharimeter.

A simple polariscope contains a fixed polarizer and a rotatable optical analyzer, with a space for a specimen between them. A historically suitable implementation uses two Nicol prisms. Each selects one linearly polarized component from the incident light through the crystal's optical action. A lamp and a collimating arrangement illuminate the first prism, and the observer examines the transmitted field through the second.

With no specimen and ideal elements, Malus's law predictswhere $I_0$ is the intensity after the polarizer and $\theta$ is the relative transmission-axis angle. Parallel settings are brightest; crossed settings give extinction. Rotating the analyser supplies an immediate check on the first element's polarization.

Insert a transparent birefringent plate between crossed elements with its principal directions oblique to their axes. The two components can acquire different phases, so they need not recombine into the original linear polarization; light can then pass the crossed analyser. With white light, wavelength-dependent retardation gives colours. Rotation of the plate, and a check without it, distinguish this response from simple sample opacity or a poor extinction adjustment. An optically active sugar solution can instead rotate the polarization plane, as in Biot's saccharimeter. The instrument therefore reveals changes of polarization through an analysed intensity, rather than making polarization directly visible to the eye.

An optically active glucose solution rotates the direction of linear polarization. With monochromatic illumination, rotating the polarimeter analyzer again produces a maximum and an extinction, but at angles shifted from the water-filled reference tube. In an ideal transparent sample, Malus's law givesThe specific rotation $[\alpha {]}_{\lambda }^T$ is defined for a stated temperature, wavelength, solvent and concentration convention. With $\ell$ in decimetres and $c$ in grams per millilitre, the conventional numerical value of $[\alpha ]$ must use the matching units. A broadband source generally gives coloured appearances because the rotation varies with wavelength; one analyser angle need not extinguish every colour.

Biot's saccharimeter is an angular polarimeter: a polarizing element, a tube of accurately known optical path length holding the sample between plane end windows, and a rotatable analysing element with an angular scale. The original arrangement used a black-glass polarizing mirror and a calcite analyser; later two-prism designs implement the same angular measurement. It should be distinguished from a later quartz-wedge compensating saccharimeter, which cancels the sample's rotation instead of directly reading the analyser rotation.^[ref]

For a historical urine estimate, clarify a sample without changing its sugar inventory, fill the tube without bubbles, make a solvent blank at the same settings, and measure the signed rotation relative to that blank. With a known dilution factor $D$ and an appropriate equilibrium glucose calibration,Repeat the reading and check a known glucose solution. Mutarotation makes the time since preparation relevant. The inference is selective only to the extent that other optically active solutes have been excluded or accounted for; a net rotation is not proof that every contribution is glucose. This is a historical analytical application, not a replacement for present clinical assessment of diabetes.