Light Propagation Through Glass

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Speed and wavelength in a medium

Light travels more slowly in glass than in vacuum. The speed in the material is c divided by the refractive index n. The frequency of the light does not change when it enters the glass. Because speed falls while frequency stays the same, the wavelength inside the glass is shorter, equal to the vacuum wavelength divided by n.

Refraction and Snell's law

When light crosses a boundary between two media, its direction changes. Snell's law states that n1 sin θ1 equals n2 sin θ2, where θ1 and θ2 are the angles measured from the normal on each side. This is the principle behind every refracting lens surface.

Dispersion revisited

Because the refractive index varies with wavelength, each colour bends by a different amount at the same surface. This is the origin of chromatic aberration. Dispersion in glass is described by the Abbe number, discussed in the glass properties article.

Absorption and scattering

Glass absorbs some wavelengths, particularly in the ultraviolet and infrared, depending on its composition. Imperfections and bubbles scatter light and reduce contrast. Good optical glass is melted and annealed to minimise both effects, and manufacturers specify transmission for each glass type.

Common mistakes

Assuming the wavelength in glass equals the vacuum wavelength. Using the incident angle directly when the refracted angle is needed. Ignoring absorption in thick elements or in applications that use the ultraviolet or infrared.

Why speed in glass varies with colour

The speed of light in glass depends on wavelength, because the refractive index depends on wavelength. Blue light travels more slowly in glass than red light. This wavelength dependence is the underlying cause of dispersion, and it is why a prism spreads white light into a spectrum.

Total internal reflection

When light travels from a medium of higher index to one of lower index, it can be totally reflected at the boundary if the angle of incidence is above the critical angle. This effect guides light inside optical fibres and prisms, and it is used in some binoculars and periscopes. The critical angle depends on the two refractive indices, and Snell's law gives it directly.

A worked example

Light at 550 nanometres in a glass with refractive index 1.5 has a wavelength of about 367 nanometres. Its speed is about two thirds of its speed in vacuum. The frequency is unchanged, so the energy per photon is unchanged, but the spacing between wave crests is shorter. This is why glass thickness, rather than optical path length, must be considered when calculating phase differences in coatings and interferometers.

Refraction at a curved surface

A curved lens surface refracts each ray according to Snell's law at the local angle of incidence. Rays far from the axis meet the surface at larger angles, which is one source of aberrations. The surface curvature, the refractive index and the position of the ray determine how it is bent.

Absorption and the Beer-Lambert law

Light intensity falls exponentially as it travels through an absorbing medium. The relation is known as the Beer-Lambert law, and it means that transmission through a thick glass element depends on both the absorption coefficient and the thickness. This is why thick lenses for ultraviolet or infrared work are made from specially purified glass.

Measuring refractive index

Refractive index can be measured with a refractometer, by observing the deviation of a light beam through a prism of the material, or by interferometry. Each method gives a value at a stated wavelength and temperature. Index data for a glass should always include both.

Refraction in everyday objects

The same physics explains why a straw looks bent in a glass of water, why a pool looks shallower than it is, and why a prism separates white light. In each case, the change in direction at a surface follows Snell's law, and the amount of change depends on the refractive indices of the two media and the angle of incidence.

Dispersion and everyday effects

The variation of refractive index with wavelength explains rainbows in water droplets and the colour separation at the edges of simple lenses. Both are caused by the same wavelength dependence, which is why colour correction in lens design is a central problem.

Choosing an optical material for a task

For ultraviolet work, choose a material with high transmission at the wavelength of interest, since many common glasses absorb strongly there. For infrared work, a different material set may be needed. The index, dispersion and transmission data should all be checked for the chosen wavelength range.

Going further

The rules in this article apply to any transparent material, so they also explain effects in water, plastics and air layers. Once the principle is understood, the same reasoning can be applied to many everyday optical problems.

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 Wave Physics summary to read the related articles.

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