Theory
Optical activity is a type of birefringence. Any linear polarization of light can be written as an equal combination of right-hand (RHC) and left-hand circularly (LHC) polarized light:
where is the electric field of the light. The relative phase between the two circular polarizations, sets the direction of the linear polarization to . In an optically active material, the two circular polarizations experience different refractive indices. The difference in the indices quantifies the strength of the optical activity,
- .
This difference is a characteristic of the material (for substances in solution, it is given as the specific rotation). After traveling through length of material, the two polarizations pick up a relative phase of
- ,
where is the wavelength of the light (in vacuum). As a consequence, the final polarization is rotated to angle .
In general, the refractive index depends on the wavelength (see dispersion). The variation in rotation with the wavelength of the light is called optical rotatory dispersion (ORD). ORD spectra and circular dichroism spectra are related through the Kramers–Kronig relations. Complete knowledge of one spectrum allows the calculation of the other.
In summary, the degree of rotation depends on the color of the light (the yellow sodium D line near 589 nm wavelength is commonly used for measurements), the path length and the properties of the material (e.g., or specific rotation and concentration).
Read more about this topic: Optical Rotation
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