Refractive Index, Abbe Value and Dispersion Formula

The optical properties are defined by two primary parameters, the refractive index and Abbe number. The refractive index is a measure of the bending power of a light beam when passing from one medium into another. The Abbe or v-number named after German physicist Ernst Abbe, is a measure of the dispersive power and is defined as:

Where n_d, n_F and n_C are the refractive indices of the material at wavelengths of the Fraunhofer d-, F- and C- spectral lines (587.6 nm, 486.1 nm and 656.3 nm respectively). Besides , the dispersion based on e-line is often used as: 

Table 1 shows some basic information of glass code, two primary optical parameters and density. Table 2 shows spectral lines and designated letters for them. The refractive indices of optical glasses are given at these wavelengths with the N-BK7 as an example.

The refractive index at a wavelength other than the spectral lines can be calculated from a dispersion formula. SCHOTT uses Sellmeier dispersion formula:

where λ is the wavelength in um ,and B₁, B₂, B₃, C₁, C₂ and C₃ are coefficients to be determined for each optical glass type. Table 3 gives the parameters of N-BK7 and N-SF11. HOYA’s dispersion formula is derived from a series expansion of the theoretical formula:

where λ is the wavelength in um ,and A₀, A₁, A₂, A₃, A₄ and A₅ are coefficients. The accuracy of both formulas for calculating refractive index at a wavelength in the visible and near infrared range has an order of 10^-6.

Properties:  

• Refractive Index, Abbe Value and Dispersion Formula
• Transmittance
• Temperature Coefficient of Refractive Index (dn/dT) (Source: SCHOTT North America, Inc.)
• Glass Designations
• Thermal Properties
• Chemical properties (Source: SCHOTT North America, Inc.)
• Mechanical Properties (Source: SCHOTT North America, Inc.)
• Abbe Diagram (n_d-v_d) Graphic (Source: SCHOTT North America, Inc.)
• N-BK7 Datasheet (Source: SCHOTT North America, Inc.)