Angular dispersion

Because of its wavelength-dependent refractive index (dispersion), a prism splits white light into its spectral colors .

Angular dispersion is a term used in optics and is a measure of the wavelength splitting of a polychromatic wave (for example a light beam of white light) by a prism or optical grating .

The change in the angle of reflection according to the wavelength is defined as the angular dispersion : ${\displaystyle \beta }$ ${\displaystyle \lambda }$ ${\displaystyle w_{D}}$

${\displaystyle w_{D}={\frac {\mathrm {d} \beta }{\mathrm {d} \lambda }}}$

The formula for a prism can be

${\displaystyle w_{D}={\frac {2\sin(\epsilon /2)}{\sqrt {1-n^{2}\sin ^{2}(\epsilon /2)}}}{\frac {\mathrm {d} n}{\mathrm {d} \lambda }}}$

derive. Here is the prism angle of an isosceles prism and n is the wavelength-dependent refractive index . The spectral dispersion depends only on the wavelength itself and the material of the prism. The angular dispersion, on the other hand, depends on the prism angle , but not on the size of the prism or the angle of incidence . ${\displaystyle \epsilon }$ ${\displaystyle {\frac {\mathrm {d} n}{\mathrm {d} \lambda }}}$

Individual evidence

1. ↑ Gerold Wünsch: Optical analysis methods for the determination of inorganic substances . Walter de Gruyter, 1976, ISBN 3-11-083203-8 , p. 89 ( limited preview in Google Book search).
2. ↑ Wolfgang Demtröder: Laser spectroscopy: Basics and techniques . 4th edition. Springer, Berlin 2004, ISBN 3-540-64219-6 , pp. 86 ( limited preview in Google Book search).