Wavelength
General media

The speed of a wave depends upon the medium in which it propagates. In particular, the speed of light in a medium is less than in vacuum, which means that the same frequency will correspond to a shorter wavelength in the medium than in vacuum, as shown in the figure at right.

This change in speed upon entering a medium causes refraction, or a change in direction of waves that encounter the interface between media at an angle. For electromagnetic waves, this change in the angle of propagation is governed by Snell's law.

The wave velocity in one medium not only may differ from that in another, but the velocity typically varies with wavelength. As a result, the change in direction upon entering a different medium changes with the wavelength of the wave.

For electromagnetic waves the speed in a medium is governed by its refractive index according to

where c is the speed of light in vacuum and n (λ) is the refractive index of the medium at wavelength λ, where the latter is measured in vacuum rather than in the medium. The corresponding wavelength in the medium is

When wavelengths of electromagnetic radiation are quoted, the wavelength in vacuum usually is intended unless the wavelength is specifically identified as the wavelength in some other medium. In acoustics, where a medium is essential for the waves to exist, the wavelength value is given for a specified medium.

The variation in speed of light with wavelength is known as dispersion, and is also responsible for the familiar phenomenon in which light is separated into component colours by a prism. Separation occurs when the refractive index inside the prism varies with wavelength, so different wavelengths propagate at different speeds inside the prism, causing them to refract at different angles. The mathematical relationship that describes how the speed of light within a medium varies with wavelength is known as a dispersion relation.
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