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Specific rotation is an intensive property, distinguishing it from the more general phenomenon of optical rotation. As such, the observed rotation ( α ) of a sample of a compound can be used to quantify the enantiomeric excess of that compound, provided that the specific rotation ( [α] ) for the enantiopure compound is known.
Optical rotation, also known as ... if the color and path length are fixed and the specific rotation is known, the observed rotation can be used to calculate the ...
[citation needed] This dependence of specific rotation on wavelength is called optical rotatory dispersion. In all materials the rotation varies with wavelength. The variation is caused by two quite different phenomena. The first accounts in most cases for the majority of the variation in rotation and should not strictly be termed rotatory ...
the specific rotation of (S)-2-ethyl-2-methyl succinic acid is found to be dependent on concentration; in what is known as the Horeau effect [3] the relationship between mole based ee and optical rotation based ee can be non-linear i.d. in the succinic acid example the optical activity at 50% ee is lower than expected.
The specific rotation [] is a physical property and defined as the optical rotation α at a path length l of 1 dm, a concentration c of 10 g/L, a temperature T (usually 20 °C) and a light wavelength λ (usually sodium D line at 589.3 nm): [4]
The observed rotation of the sample is the weighted sum of the optical rotation of each anomer weighted by the amount of that anomer present. Therefore, one can use a polarimeter to measure the rotation of a sample and then calculate the ratio of the two anomers present from the enantiomeric excess, as long as one knows the rotation of each pure anomer.
The angle of rotation is then read from a scale. The same phenomenon is observed after an angle of 180°. The specific rotation of the sample may then be calculated. Temperature can affect the rotation of light, which should be accounted for in the calculations. [] = / where:
Below are listed the Mueller matrices for some ideal common optical elements: General expression for reference frame rotation [3] from the local frame to the laboratory frame: