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Refractive Index, Abbe Value and Dispersion Formula |
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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 nd, nF and nC 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:
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