Glass Dispersion and V Number: Clarifying the Terms

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 glass dispersion and v number formula for the materials 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 refractive index dispersion (variation of refractive index and wavelength). Named for Ernst Abbe (1840-1905), a German physicist, the abbe equation 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 what is 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  

WV3 = 0.6563 micrometers

RN1, RN2 & RN3 would be the refractive indices that correspond to these three wavelengths.

The v number formula 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)

To understand how to find v number and avoid ambiguity, when OSLO defines refractive index vs wavelength with the specific indices nd vd, nf 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 refractive index and wavelength relationship 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