Abbe number

The Abbe number (or Abbe number, symbol: ) is a dimensionless quantity used in optics for the dispersion of light as it passes through a transparent medium. The smaller the Abbe number, the greater is the dispersion. The Abbe number is named after the German physicist Ernst Abbe ( 1840-1905 ).

Basics

The strength of the refraction of light whose wavelength is of (you can also say from the light color) dependent. This is referred to as a dispersion, and is, for example, the reason for splitting a white light beam to a prism into a color spectrum. All materials for optical components ( eg lenses ) used to show a more or less strong dispersion. Therefore, optical devices such as camera lenses generally make the different colors of light different from what can be shown by colored borders to the images of object edges or colored halos around bright light sources. This aberration is called chromatic aberration.

For a complete description of the dispersion of a material ( eg, a glass type ) specifies how changes of the refractive index n of the material with variation of the frequency or wavelength of the light. It must therefore be given the function or. You can either specify the refractive indices at different fixed wavelengths or a set of coefficients of a dispersion formula as the Cauchy or the sell - Meier equation. However, for ease of calculations, it is often sufficient to describe the dispersion in the visible light range by a single parameter, namely the Abbe number.

Definition

Dimensionless Abbe number is defined as

Or

Wherein nd, nF, etc., are the refractive indices of the material at the wavelengths of Fraunhofer lines corresponding. The table opposite lists the wavelengths of some of these Fraunhofer lines in which the refractive index is usually determined. For example, nd is the refractive index at a wavelength of 587.6 nm

A low-dispersion material having a high Abbe number. The reciprocal of the Abbe number is also referred to as a relative dispersion.

The typical values ​​of the Abbe numbers for the types of glass most commonly used range from about 20 ( flint glass ) to 60 ( crown glass ). The limit for the name of the glasses as flint glass and crown glass is an Abbe number of 50 Special types of glass ( fluorite crown glass ) have ratios by 85 magnesium fluoride reaches even an Abbe number of 95, its dispersion is thus particularly low.

Application

The Abbe number is for the design of achromatic important. These are lens systems in which the chromatic aberration is very small. For example, having an achromatic of two thin lenses which have a small distance from each other for the Fraunhofer lines F and C, the same focal length, when

, wherein the Abbe numbers and the focal lengths of both lenses. Such a lens system is blue and red light of the wavelengths 486 nm ( R ) and 656 nm ( C) from the same point. The residual color error is significantly less than if only one type of glass would have been used. Achromatic lenses were the basis for the construction of large refracting telescopes in the 19th century.

The remaining when achromatic color errors ( the so-called secondary spectrum ) often manifests itself in a purple fringe around bright objects. To reduce the color aberration further, the refractive index of more than two wavelengths must be considered ( as the light is shown at the three wavelengths at a point, one has a apochromat ). Even here, helps the Abbe number to classify types of glass coarse.

In the field of infrared and ultraviolet is the Abbe number, which is of course defined for wavelengths in the visible light range, suitable.