# Optical activity

The optical activity Is a property of some transparent materials to turn the polarization direction of light. When passing linearly polarized light through a visually active medium the plane of polarization of light is rotated a little bit at each molecule. For chiral molecules, this effect occurring at each individual molecule does not average back to zero with statistical certainty, so the individual rotations can accumulate. It results after passage of the light through the entire substance body a large measurable net rotation amount.

A distinction is made between right-turning (plane of polarization observer-sided right-turning) and left-turning substances. A third category is formed by racemates in which there are always equal concentrations of the two dextrorotatory and levorotatory substances (enantiomers) and which are thus optically inactive are.

## Chemical-physical causes

### Polarized light

Light is an electromagnetic wave. With such a polarization, an electric field oscillates – d. h. the field vector describing the field strength and direction – perpendicular to the wave vector (propagation direction) of the wave. By the oscillation of the vector and the direction of propagation, therefore, a very specific plane in space is distinguished. If one looks towards the beam, one sees only the "edge" of this plane, which is inclined at a certain angle.

Normal light contains rays that oscillate in any direction, whereas linearly polarized light oscillates in only one plane. In optically active substances the inclination of this plane is changed. Thus also normal light of optically active substances is rotated, only it is not noticeable, because before as after all directions are represented. In contrast, in polarized light the change of the angle is directly measurable.

### Rotation of the polarization direction

In order to understand the phenomenon of optical activity, it is first necessary to understand why most substances have the not optically active. This is because each molecule of each compound contains centers of charge and thus an electric field that interacts with the wave and can easily rotate the plane of oscillation. The degree of this rotation depends decisively on the spatial orientation of the molecule to the wave. By the exact mirror image of a molecule (the enantiomer) a performed rotation is exactly reversed again.

In a solution, the molecules are statistically distributed by thermal motion into every possible position. So we can say that a ray rotated by a molecule will meet a molecule rotated in such a way that it exactly corresponds to the mirror image of the first one, undoing the rotation. In general, substances are not optically active. If enantiomers are present in equal amounts (1:1 mixture) and thus the rotation of the polarized light cancels itself out again, we speak of a racemate.

The reason for the optical activity of chiral substances lies exactly in the mirror image idea: according to definition they can be not by rotation to coincide with their mirror image, d. h., by rotation into its mirror image, whereby in the case of the pure enantiomer there are no mirror images and the rotation can therefore not be exactly reversed. This actually results in a macroscopic rotation of the polarization.

The designations for the directions of rotation are (+) for dextrorotatory substances or enantiomers and (-) for levorotatory substances. There are no stable, d. h. correlation, which applies to all substances, between the (R)- or. (S)-configuration (or the D- or. L configuration) of enantiomers and the direction of rotation of the linearly polarized light.

If two oppositely circularly polarized waves of the same frequency overlap, the result is a linearly polarized wave. In the case of optical activity, the opposite occurs: a linearly polarized wave is split into two circularly polarized waves, one counterclockwise and one clockwise. Optically active substances now have the property that one of these two waves has a higher propagation speed. So, at the end of the crystal, one wave has not rotated as far as the other one, the superposition of both waves results again in a linearly polarized wave (the frequency is not changed in the medium), but its electric field vector is rotated by an angle alpha.

### Specific angle of rotation

The macroscopic rotation angle $\alpha$ , which is found when linearly polarized light passes through an optically active substance, depends first on the substance itself, d. h. different molecules influence the light differently. In addition, the angle of rotation is influenced by the following factors:

• by the wavelength of the light, also Optical rotational dispersion (ORD) called
• from the temperature of the sample, which determines the thermal motion of the individual molecule
• from the number of molecules passed by the light, i.e. from the concentration of a sample and the length the light travels through the sample
• from the solvent, if it is a solution.

If the wavelength λ of the light and the temperature T are given, one can calculate the specific angle of rotation a of a substance (for this wavelength and temperature):

• the measured (non-specific) rotation angle $\alpha$
• the mass concentration $\beta$ of the solution
• of the thickness irradiated $d$ .

Usually the angle is given for yellow sodium light (λ = 589 nm or. "D" for the sodium D-line) and a temperature of 20 °C (or 25 °C):

literature values refer to the otherwise rather unusual units $\beta = 1$ (corresponding to 1 g of substance per 100 cm³ of solution) and d = 1 dm.

with circular wavenumber $k$, the rotation angle depends reciprocally on the square of the wavelength, provided that a wavelength range is considered in which the optically active substance is none Light absorbed. In the range of absorption maxima, however, the Cotton effect dominates.

### Other causes

also most crystals rotate the light, u. a. Quartz, calcite, cinnabar, and sodium chlorate. For them, the asymmetry lies in the crystal structure.

In the presence of a static magnetic field are all molecules optically active. This Faraday effect was one of the first discoveries to show a connection between light and electromagnetism.

### Rotation Angle

The angle of rotation $\alpha$ by which the plane of polarization of linearly polarized light of wavelength $\lambda$ has been rotated after passing through distance $d$ is:

where $n_\mathrm$ is the refractive index for left-handed light and $n_\mathrm$ is that for right-handed light.

## Practical meaning

Measurable is the optical activity by means of a polarimeter. From the measured angle of rotation, the concentration of a solution can be calculated with the above formula, which is used especially in sugar processing (saccharimetry). Some historical names are due to this practical application:

• Dextrose ( Latin dexter ‘right)’ is a historical name of glucose, which is dextrorotatory.
• Laevulose (Latin laevus ‘left’) is a historical name of fructose, which is levorotatory.
• Invert sugar is a mixture of glucose and fructose formed when sucrose is broken down. The direction of rotation is inverted from right to left, and the new rotation angle is the sum of the rotation angles of the glucose and fructose present in the same concentration.

Natural products often have a large number of chiral centers with unique configurations and therefore exist in the form of enantiomers. These rotate the plane of polarized light by the same amount in opposite directions (different signs) and usually have different physiological effects on living organisms. Therefore, the measurement of optical purity with a polarimeter is an important quality criterion for chiral drugs.