Math 2.0

Optics, electromagnetic theory Definition

Optical activity

Builds on Polarization of lightRefractive indexPlane wave

Definition

Let a linear transparent medium be given, and consider monochromatic plane waves of vacuum wavelength λ\lambda that travel in a fixed direction through it. The medium is optically active in that direction when, without any external magnetic field, the two circular polarizations are modes. These modes must have different refractive indices nL≠nRn_L \ne n_R. The optical rotation over a path of length dd is the angle θ=πd(nL−nR)/λ\theta = \pi d (n_L - n_R) / \lambda. It is the angle by which the direction of a linear polarization turns, with a sign convention for the sense of rotation.

Remarks

Write linear polarization as the sum of the two circular states with equal amplitudes. After the path dd their phases differ by 2πd(nL−nR)/λ2\pi d (n_L - n_R)/\lambda, and the direction of the resulting linear polarization turns by half of this, which gives θ\theta.

Example: a solution of sucrose in water is optically active. For solutions, the rotation is proportional to the path length and to the concentration, and the factor is the specific rotation of the substance.

Non-example: pure water is not optically active, since its molecules are not chiral and both circular states see the same index.

Optical activity is reciprocal: if light passes through the medium, is reflected and comes back, the two rotations cancel. This distinguishes it from the Faraday effect, where the rotations add.

Reading path

To understand this page from the ground up, read these 4 pages in order. The foundations come first.

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Plane wave, concept, no evidence levelPlane waveconceptPolarization of light, concept, no evidence levelPolarization of lightconceptRefractive index, concept, no evidence levelRefractive indexconceptOptical activity, definition, no evidence levelOptical activitydefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
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  1. Plane wave concept
  2. Polarization of light concept
  3. Refractive index concept
  4. Optical activity definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Optical_rotation
About this page
Tag40FS0HAMEC
URIm2://40FS0HAMEC
Kinddefinition
WritingW0 stub
MSC78A10
DefinesOptical activity
UsesPolarization of light, Refractive index, Plane wave
Changed3 November 2026

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