Q.A 300 mm long tube containing 60 cc of sugar solution produces a rotation of 9° when placed in a polarimeter. If the specific rotation is 60°, calculate the quantity of sugar contained in the solution.

Optical Activity and Specific Rotation

Some substances have the remarkable property of rotating the plane of vibration of plane-polarised light as it passes through them. Such substances are called optically active, and the property is optical activity. Common examples are sugar (sucrose) solutions, turpentine, and quartz crystals.

Optical rotation

Send plane-polarised light through an optically active medium and the plane of polarisation emerges turned through an angle $\theta$. Substances that rotate it clockwise (as seen by an observer facing the oncoming light) are dextrorotatory ($d$ or $+$); those that rotate it anticlockwise are laevorotatory ($l$ or $-$). The molecular origin is chirality — the molecule and its mirror image are not superimposable.

Specific rotation

The angle of rotation for a solution depends on how much active substance the light passes through — on both the path length and the concentration — so we define a standardised quantity, the specific rotation $[\alpha]$:

• $\theta$ = observed angle of rotation (degrees)
• $l$ = length of the solution column the light traverses (usually in dm)
• $C$ = concentration of the solution (g per mL, or g per cm³)
• $T,\ \lambda$ = the temperature and wavelength of light at which it is measured (it depends on both) …