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
Famous quotes containing the word theory:
“By the “mud-sill” theory it is assumed that labor and education are incompatible; and any practical combination of them impossible. According to that theory, a blind horse upon a tread-mill, is a perfect illustration of what a laborer should be—all the better for being blind, that he could not tread out of place, or kick understandingly.... Free labor insists on universal education.”
—Abraham Lincoln (1809–1865)
“No one thinks anything silly is suitable when they are an adolescent. Such an enormous share of their own behavior is silly that they lose all proper perspective on silliness, like a baker who is nauseated by the sight of his own eclairs. This provides another good argument for the emerging theory that the best use of cryogenics is to freeze all human beings when they are between the ages of twelve and nineteen.”
—Anna Quindlen (20th century)
“... liberal intellectuals ... tend to have a classical theory of politics, in which the state has a monopoly of power; hoping that those in positions of authority may prove to be enlightened men, wielding power justly, they are natural, if cautious, allies of the “establishment.””
—Susan Sontag (b. 1933)