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Q&A: Clarifying use of the terms “dispersion” and “V-number”

Question
I notice that when I edit my wavelengths in OSLO, the V-number of my glasses seems to change. I thought that the V-number of a glass was calculated based on certain set wavelengths and was independent of the wavelengths you model the glass for. How does OSLO define dispersion and V-number for the glasses it models?

Synopsis
Clarifying use of the terms “dispersion” and “V-number”

Solution
Abbe Number, also known as the V-number of a transparent material is a measure of the material’s dispersion (variation of refractive index with wavelength). Named for Ernst Abbe (1840-1905), a German physicist, the Abbe Number is usually defined as
V = (nd – 1)/(nF – nC) where nd, nF and nC are the refractive indices of the material at the wavelengths of the Fraunhofer d-, F- and C- spectral lines (587.6 nm, 486.1 nm and 656.3 nm respectively).

In some regions of the world, the preference is to use the Fraunhofer D- spectral line (589.3 nm) in place of d- to calculate V-number this can cause confusion.

Important: When users enter three or more wavelengths into OSLO, it is assumed that the users enter the first three wavelengths in the following order: middle, low & high.

EXAMPLE:
If the wavelengths 486.1 nm, 587.6 nm, and 656.3 nm are entered into OSLO, they should be entered in the following order:
WV1 = 0.5876 micrometers
WV2 = 0.4861 micrometers
WV2 = 0.6563 micrometers
RN1, RN2 & RN3 would be the refractive indices that correspond to these three wavelengths.

The V-number discussion above is really only valid for calculations in the visible region of the wavelength band. OSLO extends the calculations to utilize the wavelengths entered by the user. The general V-number as defined in OSLO is given the term VNBR and is defined by the following equation:
VNBR = (RN1-1)/(RN2-RN3)In order to avoid ambiguity, when OSLO defines V-number with the specific refractive indices nd, nF and nC, OSLO uses the term Vd: Vd = (nd – 1)/(nF – nC) Important: This means that if WV1, WV2 or WV3 changes in your lens model, the calculation of VNBR will change, but the calculation of Vd will not change.

In the OSLO documentation (online help and manuals), the generic term “dispersion” is often used. This, of course, refers to the change of refractive index with a wavelength in optical materials. Occasionally, the OSLO documentation uses the term Dispersion as a specific mathematical function. When this is the case, Dispersion is defined as Dispersion = nF – nC

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