AbbeZahl

The Abbe number, also known as the V-number or constringence, is a dimensionless quantity used in optics to describe the dispersion of a transparent material. It is defined as the reciprocal of the relative partial dispersion. The Abbe number is typically denoted by the Greek letter nu ($\nu$) and is calculated using the refractive indices of the material at specific wavelengths. The standard wavelengths used are those corresponding to the Fraunhofer lines: the hydrogen F line (blue, 486.13 nm), the helium d line (yellow, 587.56 nm), and the hydrogen C line (red, 656.27 nm).

The formula for the Abbe number is: $\nu = \frac{n_d - 1}{n_F - n_C}$, where $n_d$, $n_F$, and $n_C$ are the refractive indices at the helium d, hydrogen F, and hydrogen C lines, respectively. A higher Abbe number indicates lower dispersion, meaning the material separates light of different wavelengths less. Conversely, a lower Abbe number signifies higher dispersion. Materials with high Abbe numbers are desirable for optical components like lenses where chromatic aberration needs to be minimized, as they refract different colors of light very similarly. Crown glasses typically have high Abbe numbers, while flint glasses have lower Abbe numbers and exhibit greater dispersion. The Abbe number is a crucial parameter in the design of achromatic lenses and other optical systems.