Optical Glass and Refraction

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Refractive index

The refractive index of a material is the ratio of the speed of light in vacuum to its speed in the material. Glass used in lenses typically has an index between about 1.5 and 2.0, depending on its composition. A higher index allows a surface to bend light more strongly, so an element can be thinner or have a gentler curve for the same effect.

Dispersion and the Abbe number

Dispersion is the variation of refractive index with wavelength. It is quantified by the Abbe number, V, which is calculated from the refractive indices at three standard wavelengths: V = (nd − 1) divided by (nF − nC). Glasses with a high Abbe number disperse light less, and glasses with a low Abbe number disperse it more.

Crown glasses generally have a high Abbe number and low dispersion. Flint glasses generally have a low Abbe number and higher dispersion. Designers combine the two to correct chromatic aberration, as described in the chromatic aberrations article.

Choosing glass in practice

Glass choice balances optical performance against cost, weight, density, temperature behaviour and chemical stability. Some specialised glasses offer very low dispersion but are expensive or sensitive to heat. Designers select the glass for each element according to its job in the lens.

Coatings

Surfaces reflect a small fraction of the light that reaches them. Anti-reflection coatings reduce this reflection, which improves contrast and reduces ghosting. A simple coating relies on thin-film interference, described in the interference article.

Common mistakes

Comparing refractive indices without considering dispersion. Assuming a high index is always better: it can come with higher dispersion or lower stability. Forgetting that glass properties depend on wavelength and temperature.

Measuring refractive index

Refractive index is usually specified at a standard wavelength, commonly the sodium d line at 587.6 nanometres. Manufacturers also specify index at the F and C spectral lines, from which the Abbe number is calculated. Measurements are made under controlled temperature, because index changes slightly with temperature.

Glass selection for a design

A designer typically starts by choosing a crown and a flint with suitable indices and dispersions, then adjusts the curvatures and spacing to meet the target focal length and image quality. Glass catalogues list indices, dispersions and other properties for each type, along with transmission and stability data. The choice affects cost, weight, temperature sensitivity and how easily the glass can be processed.

Handling and environmental stability

Some optical glasses are sensitive to humidity, temperature or chemical attack, and they must be protected during manufacture and use. Coatings and sealed mounts help. Designers consider these effects when they choose materials for lenses intended for outdoor, marine or high-temperature use.

Glass families and naming

Optical glasses are classified by their refractive index and Abbe number, and manufacturers give each glass a catalogue code that reflects these values. The codes are useful for finding equivalent glasses from different suppliers, but designers still check the full data sheet, including transmission, stability and processing properties.

Transmission and absorption

Optical glass transmits most of the visible spectrum, but absorption increases at the ultraviolet and infrared ends. Some glasses are chosen for their transmission at specific wavelengths, such as the near infrared used in some sensing systems. Thick elements absorb more than thin ones, so transmission must be considered in the design.

Stress and birefringence

Mechanical stress in glass changes its refractive index slightly in different directions, which is called birefringence. Stress can come from mounting, from thermal changes or from manufacturing. Birefringence can reduce image quality, particularly in polarised light. Careful mounting and annealing reduce the problem.

Questions to ask a glass supplier

Ask for the refractive index and Abbe number at the wavelengths you need, the transmission curve, the stability under temperature and humidity, and the homogeneity specification. Ask whether the glass is stress-annealed, and what the maximum allowable birefringence is. These questions turn a catalogue entry into a specification you can test against.

Glass in lens and prism design

Lenses use glass where high transmission and low distortion matter. Prisms in binoculars and cameras use glass where total internal reflection is needed. The same index data guides both, but the criteria differ: a lens needs low dispersion and good homogeneity, while a prism needs a stable index and freedom from internal stress.

Temperature dependence

Refractive index changes slightly with temperature, and the change differs between glasses. In a precision optical system, this can shift focus over a temperature range. Designers choose glasses with suitable temperature coefficients, or add compensating elements.

Going further

Glass properties are specified with care because small differences in index or dispersion can change the final image. The data sheet is therefore the reference for any design decision, not a summary to skim.

Summary

The key point of this article is the one stated at its start. Check the formula, use the stated assumptions, and confirm any result with a test before relying on it in practice.

Sources

• Eugene Hecht, Optics, Pearson (any current edition).
• Max Born and Emil Wolf, Principles of Optics, Cambridge University Press (any current edition).
• ISO 12233: Photography, Electronic still picture imaging, Resolution and spatial frequency responses.

Next step

Return to the pillar guide or the Lens Design summary to read the related articles.

General information only. This page explains optical principles and does not replace lens design work, lens testing or advice from a qualified optical engineer.