Past exam of the medicine course of the University of Oxford / 1866 / First examination / Physics / 7 / Solution

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.