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For visible applications, the Abbe number for a glass is of equal practical importance as the refractive index itself. The Abbe diagram is a simple graphic tool that captures the basic refractive properties of a wide range of optical glasses. It comprises a simple 2D map with the horizontal axis corresponding to the Abbe number and the vertical axis to the glass index. A representative diagram is shown in Figure 4.24.

By referring to this diagram, the optical designer can make appropriate choices for specific applications in the visible. In particular, it helps select combinations of glasses leading to a substantially achromatic design. One special and key application is the achromatic doublet. This lens is composed of two elements, one positive and one negative. The positive lens is a high power (short focal length) element with low dispersion and the negative lens is a low power element with high dispersion. Materials are chosen in such a way that the net dispersion of the two elements cancel, but the powers do not. This will be considered in more detail in the next section.

The different zones highlighted in the Abbe diagram replicated in Figure 4.24 refer to the elemental composition of the glass. For example, ‘Ba’ refers to the presence of barium and ‘La’ to the presence of lanthanum. Originally, many of the dense, high index glasses used to contain lead, but these are being phased out due to environmental concerns. The Abbe diagram reveals a distinct geometrical profile with a tendency for high dispersion to correlate strongly with refractive index. In fact, it is the presence of absorption features within the glass (at very much shorter wavelengths) that give rise to the phenomenon of refraction and these features also contribute to dispersion.