Spectrum

The modern term spectrum (plural: spectra) signifies an entity which can vary widely within a continuum rather than just taking specific limited values. The word has evolved from the old English word spectre meaning a ghost or apparition, but the modern meaning now comes from its use within science.

Originally introduced within optics to describe the sprectrum of light (visible within the rainbow or using a prism), it has since been applied by analogy to many fields. Thus one might talk about the spectrum of political opinion, or of human sexuality, or the spectrum of activity of a drug, or the autistic spectrum. In these uses, the implication is, a broad range of varied conditions or behaviors, grouped together and studied under a single title for ease of discussion.

In most modern usages of the word, there is a unifying theme of between extremes at either end. Older usages did not emphasize unifying theme, but nonetheless led to the modern ones through a sequence of events set out below. Some modern usages in mathematics evolved out of a unifying theme (of cases) but may be difficult to recognize as fitting into it.

Origins
Originally a spectrum was what is now called a spectre, i.e., a phantom or apparition. Spectral evidence is testimony about what was done by spectres of persons not present physically, or hearsay evidence about what ghosts or apparitions of Satan said. It was used to convict a number of persons of witchcraft at Salem, Massachusetts in the late 17th century.

Modern (17th through 21st centuries) meaning in the physical sciences
In the 17th century the word spectrum was introduced into optics, referring to the range of colors observed when white light was dispersed through a prism. Soon the term referred to a plot of light intensity as a function of frequency or wavelength. Max Planck later realized that frequency represents electromagnetic energy:


 * $$ E = h \nu $$

where E is the energy of a photon, h is Planck's constant, and $$ \nu $$ is the frequency of the light.

The word spectrum then took on the obvious analogous meaning in reference to other sorts of waves, such as sound wave, or other sorts of decomposition into frequency components. The plural of the word "spectrum" is "spectra", as in, "Let us consider the power spectra of the following electronic signals...". Thus a spectrum is a usually 2-dimensional plot, of a compound signal, depicting the components by another measure. Sometimes, the word spectrum refers to the compound signal itself, such as the "spectrum of visible light", a reference to those electromagnetic waves which are visible to the human eye. Looking at light through a prism separates visible light into its colors according to wavelength. Violet at one end has the shortest wavelength and red at the other end has the longest wavelength of visible light. The colors in order are violet, blue, green, yellow, orange, red. As the wavelengths get bigger below the red visible light they become infrared, microwave, and radio. As the wavelengths get smaller above violet light, they become ultra-violet, x-ray, and gamma ray.

See electromagnetic spectrum.