Number of Abbot

In Optical, and more particularly in spectacle industry, the number of Abbot or constringence of a optical Verre is used to determine the Dispersion of it, i.e. the variation of the Index of refraction with the Wavelength. It quantifies the Chromatic aberration transverse of an optics.

A diagram of Abbot is a Diagramme number of Abbot-index of refraction.

The name was given in the honor of the Physicien Ernst Abbe which defined the constringence.

Definition

The number of Abbot is defined according to the indexes of refraction in different wavelengths, corresponding to lines spectral of Fraunhofer of some elements:
V = \ frac {n_ \ mathrm {D} - 1} {n_ \ mathrm {F} - n_ \ mathrm {C}}
where the indices are
  • N D, in the line D of the Hélium to 589,2 Nm
  • N F, in the line F of the Hydrogène to 486,1 Nm
  • N C, in the line C of hydrogen with 656,3 Nm
Other definitions are sometimes used where:
  1. N D is taken in the line D of helium with 587,6 Nm
  2. N D is taken in the line E of the mercury to 546,1 Nm, and N F and N C respectively in the lines of the Cadmium to 480,0 and 643,8 Nm.

Properties

More the constringence is high minus glass present of chromatic dispersion. The number of Abbot can be expressed like the relationship between the principal Angle of Réfraction and the angle of Dispersion.

The diagram of Abbot is a Digramme constringence-index of refraction (See figure 1). It is used to compare various types of glass.

Applications

The number of Abbot is used to minimize the chromaticity of a system of lenses. For a system of two coupled lenses of focal F 1 and F 2 and constringences V 1 and V 2, the empirical condition of minimization is
\, f_1 V_1 + f_2 V_2 = 0.
It ensures that the focal distance from the system is the same one in the lines F and C. By supposing that the index of refraction is a smooth function wavelength, that implies that the focal distance is about constant on the interval 480-560 Nm, in other words that optics is achromatic.

This principle was used in the design of large the telescopes with the XIXe century.

It will be noted that:

  1. the number of Abbot is defined for optics in the visible one and does not allow to quantify chromaticity in the Ultraviolet or the Infrarouge;
  2. the constringence compares two wavelengths given and does not allow to describe in detail what occurs on the interval from wavelength.

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