Mathematically,

at temperature t

where [α] is the constant of proportionality

 The constant of proportionality [α] is called specific rotation and is defined as the optical rotation in degrees of the plane of polarization of a ray of monochromatic light that passes through a tube 1 decimeter long containing the substance in solution at a concentration of 1 gram per millimeter in a polarimeter.

An enantiomer will thus rotate the plane of polarized light either clockwise or anticlockwise. The clockwise rotation is usually denoted by either of the prefix dextro or (+). Similarly anticlockwise rotation is denoted by laevo or (-).  Thus, an equimolar mixture will not give any optical rotation at all. Such a mixture is referred to as a racemic mixture.

Whether a particular sample consists of a single enantiomer or a mixture of enantiomers can be determined by its observed specific rotation. For example, an enantiomerically pure sample-meaning only one enantiomer is present-of (S)-(+)-2-bromobutane will have an observed specific rotation of +23.1° because the specific rotation of (S)-(+)-2-bromobutane is +23.1°. If, however, the sample of 2-bromobutane has an observed specific rotation of 0°, we will know that the compound is a racemic mixture. If the observed specific rotation is positive but less than +23.1°,  we will know that we have a mixture of enantiomers and the mixture contains more of the enantiomer with the S configuration than the enantiomer with the R configuration. From the observed specific rotation, we can calculate the optical purity of the mixture.

 

For example, if a sample of 2-bromobutane has an observed specific rotation of +9.2°, its optical purity is 0.40. In other words, it is 40% optically pure-40% of the mixture consists of an excess of a single enantiomer.

Because the observed specific rotation is positive, we know that the solution contains excess (S)-(+)-2-bromobutane. The enantiomeric excess (ee) tells us how much excess (S)-(+)-2-bromobutane is in the mixture. As long as the compound is chemically pure, enantiomeric excess and optical purity will be the same.