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Abbe Number

Abbe number is related to the optics, which is a growing branch of physics. The field of optics impacts an ever expanding range of applications in physics, engineering and technology. The parallel emergence of lasers, fiber optics, nonlinear devices, and a variety of semiconductor sources and detectors in the 1960's initiated a continuing period of rapid development in applied and theoretical optics. The need for a variety of updated optics texts with different approaches and emphases is apparent, both for students of optics and for practitioners who need an occasional review of the basics.

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Definition

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The Abbe number is nothing but a measure of the dispersion of a material connected to the refractive index of that material. Ernst Abbe (1840-1905), the German physicist found this and it is named after him. The Abbe number of a material is defined as,

$V$ = $\frac{n_{d}-1}{n_{F}-n_{C}}$

Where $n_{d}$, $n_{F}$, $n_{C}$ are the refractive indices of the material at the wavelengths of the $d-,\ F-$ and $C-$ spectral lines (587.6 nm, 486.1 nm and 656.3 nm respectively).

Abbe Value of Lenses

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The Abbe value indicates the ability of a lens material to purely refract white light without chromatic aberration. It is sometimes referred to as the Nu value, and runs between 1 and 100. The closer the Abbe number is to 100, the more efficient the lens  material. A high Abbe number indicates that the material is not likely to cause chromatic problems when viewing objects through portions of the lens other than the optical center. A low Abbe number indicates that the material could cause chromatic distortion problems. The given table describes the lens material and its Abbe number. 

Abbe Values of Common Lens Materials

 Material   Index 
 Glass, crown     59 
 CR-39    58 
 Spectralite    47 
 High index 1.56 (resin)     39 
 High index 1.60 (resin)    37
 High index 1.66(resin)    32
 Polycarbonate    31 
 High index glass    25 


Abbe Prism

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The Abbe prism shown in the figure consists of a block of glass forming a right prism with 30°-60°-90° triangular faces. When in use, a bundle of collimated white rays is refracted at face EF, undergoes total internal reflection at face FG, and is refracted once again on exiting face EG. The prism shown below is designed in such a way that only one particular wavelength of the incident light exits the prism at a deviation angle of exactly 60°. By rotating the prism ( in the plane of the page) around any point Oel on the face EF, the wavelength which is deviated by 60° is isolated from the other wavelengths in the bundle and can thus be separately observed. 

Abbe Prism

Abbe Refractometer

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In principle, it measures the angle of incidence required to just begin total internal reflection for light propagating from a standard glass hemisphere of high index to a sample of lower index. In practice, due to easier alignment of the beams, the light is incident  in the reverse direction into the interface between the sample and the glass hemisphere. Accurate measurement of refractive index using this instrument, however, requires a good contact between the sample surface and the top surface of the prism of the instrument. Often, if the sample surface is not perfectly smooth and flat, a small amount of index-matching liquid will be used to improve the quality of the refracted signal. The index of the oil is chosen to be near that of the sample. However, as the sample index is measured, the index liquid should be changed to match the unknown more closely in order to obtain a good measurement. The only time we have found this method to be lacking is in the measurement of porous glass samples, due to an infiltration of the index matching oil into the sample pores.  

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