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For a given substance, the angle by which the polarization of light of a specified wavelength is rotated is proportional to the path length through the material and (for a solution) proportional to its concentration. Optical activity is measured using a polarized source and polarimeter.
This angle is determined with a rotatable polarizing filter (7). In chemistry, specific rotation ([α]) is a property of a chiral chemical compound. [1]: 244 It is defined as the change in orientation of monochromatic plane-polarized light, per unit distance–concentration product, as the light passes through a sample of a compound in solution.
Determination of specific rotation: In order to determine a specific rotation of an optically active substance (say, sugar), the polarimeter tube is first filled with pure water and the analyzer is adjusted for equal darkness (both the halves should be equally dark) point. The position of the analyzer is noted with the help of the scale.
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 standard translational model of Brownian motion. Much like translational diffusion in which particles in one area of high concentration slowly spread position through random walks until they are near-equally distributed over the entire space, in rotational diffusion, over long periods of time the directions which these particles face will spread until they follow a completely random ...
To orient such an object in space requires three angles, known as Euler angles. A special rigid rotor is the linear rotor requiring only two angles to describe, for example of a diatomic molecule. More general molecules are 3-dimensional, such as water (asymmetric rotor), ammonia (symmetric rotor), or methane (spherical rotor).
Molecular geometries can be specified in terms of 'bond lengths', 'bond angles' and 'torsional angles'. The bond length is defined to be the average distance between the nuclei of two atoms bonded together in any given molecule. A bond angle is the angle formed between three atoms across at least two bonds.
Figure 1: Euler's rotation theorem. A great circle transforms to another great circle under rotations, leaving always a diameter of the sphere in its original position. Figure 2: A rotation represented by an Euler axis and angle. In three dimensions, angular displacement is an entity with a direction and a magnitude.