Dispersion prism

Dispersion prisms are a group of optical prisms whose function is based on the dependence of refraction on the wavelength of light. Among other things, they are used to generate light spectra , for example in a prism spectrometer .

How it works and types

Color dispersion through a 60 ° prism

If a light beam falls on the interface between air and prism, the light beam is refracted due to the different propagation speed of the light in the media . In a medium with non-zero dispersion , the refractive index depends on the wavelength of the light. Therefore, in a multi-colored light beam, each wavelength experiences a different deflection. The refracted light therefore spreads from the entry point as a diverging light bundle.

Analogously, this effect also takes place on the exit surface of the light beam. This leads to the fact that the beam divergence and splitting cancel each other out with parallel entry and exit surfaces. In a dispersion prism, the entry and exit surfaces are inclined in relation to one another, so that a diverging bundle of rays and a spectral split occur after passage.

The simplest and at the same time frequently used form of a dispersion prism is an optical prism with a triangular cross-sectional area. In addition, there are a number of other geometries that are used as dispersion prisms. These also include prisms in which the light beam is reflected on one or more surfaces (metallic reflection and also total reflection ), for example the Littrow prism or the Pellin-Broca prism .

Dispersion prisms of special design are, for example:

• The straight vision prism consists of a series of simple triangular prisms with different material properties.
• The Pellin-Broca prism is a square prism with an additional internal total reflection for 90 ° deflection of the diverging light beam. It is suitable as a Brewster prism for the loss-free deflection of linearly polarized light.

Applications

Monochromator

Dispersion prisms are used in spectrometers to generate a constant, minimal deflection for a specific wavelength. Due to the spectral splitting of the light, a specific wavelength can be selected after passing through the prism, for example using a slit diaphragm . By rotating the prism in the cross-sectional plane, the wavelength of the light can also be changed with minimal deflection and can therefore be used as a monochromator (prism monochromator ). Examples are the Littrow prism and the Pellin-Broca prism .

In a similar function, dispersion prisms are used in modern spectral ellipsometers to achieve shorter measurement times for a spectrum; they do not initially generate monochromatic light that is then radiated onto the sample, but instead become multicolored light after it has been reflected from the sample in a prism Spectrally split and the individual colors measured simultaneously via a CCD line.

Deflection of monochromatic light

To determine the dispersion of a material, the deflection of various monochromatic light is measured. A ray of such light emerges from the prism undivided. Its exit angle and thus its deflection are clear. For appropriate measurements, the symmetrical light passage is used, where the deflection is minimal and can be described with the following simple formula:

${\displaystyle n={\frac {\sin {\frac {\delta _{\min }+\varepsilon }{2}}}{\sin {\frac {\varepsilon }{2}}}}}$

with: n = refractive index of the material for the light used

${\displaystyle \delta _{\min }}$ = minimum deflection angle

${\displaystyle \varepsilon }$ = Prism angle at the refracting edge

A corresponding measuring device is a goniometer spectrometer.

Combination of individual dispersion spectra

By combining two or more dispersion prisms, in addition to the spectral splitting of the light, further functions can be implemented, for example an overall achromatic behavior or a behavior that is not deflecting for a specific wavelength.

Achromatic behavior in a prism means that after passing through the arrangement there is no angular dispersion for different wavelengths, that is, the differently colored light rays do not diverge further, but run parallel to each other. This can be achieved, for example, by combining a 60 ° prism made of crown glass and half a 60 ° prism made of flint glass . A dispersion prism with this effect is called an achromatic prism .

Other combinations, however, can be used as a straight vision prism . With this type of dispersion prism, a negligible deflection is achieved for a given wavelength. However, the angular dispersion is retained. A typical arrangement is a row of simple triangular prisms with different materials, for example crown and flint glass.

Individual evidence

1. ↑ Eugene Hecht: Optics . Oldenbourg Wissenschaftsverlag, 2005, ISBN 978-3-486-27359-5 , p. 307-310 .
2. ^ ^{A b c} F. Pedrotti, L. Pedrotti, W. Bausch: Optics for engineers: Fundamentals . Springer, 2005, ISBN 978-3-540-22813-4 , pp. 167-168 .
3. ↑ Derivation of the formula with minimal distraction - Doris Samm
4. ↑ Goniometer spectrometer: light of different wavelengths is generated by a spectral lamp. One observes the deflection of various Fraunhofer lines in the lamp spectrum. ( Link to the goniometer spectrometer )
5. ↑ ^{a b} Ludwig Bergmann , Heinz low , Clemens Schaefer (eds.): Textbook of experimental physics: Optics: Wave and particle optics . Walter de Gruyter, 2004, ISBN 978-3-11-017081-8 , p.  213-216 .
6. ^ Helmut Lindner, Wolfgang Siebke: Physics for engineers . Hanser Verlag, 2006, ISBN 978-3-446-40609-4 , pp. 361-362 .

literature

• Eugene Hecht: optics . Oldenbourg Wissenschaftsverlag, 2005, ISBN 978-3-486-27359-5 , p. 307-311 .