Dispersion, the separation of visible light into a spectrum, may be accomplished by means of a prism or a diffraction grating. Each different wavelength or frequency of visible light corresponds to a different color, so that the spectrum appears as a band of colors ranging from violet at the short-wavelength (high-frequency) end of the spectrum through indigo, blue, green, yellow, and orange, to red at the long-wavelength (low-frequency) end of the spectrum. In addition to visible light, other types of electromagnetic radiation may be spread into a spectrum according to frequency or wavelength.
The spectrum formed from white light contains all colors, or frequencies, and is known as a continuous spectrum. Continuous spectra are produced by all incandescent solids and liquids and by gases under high pressure. A gas under low pressure does not produce a continuous spectrum but instead produces a line spectrum, i.e., one composed of individual lines at specific frequencies characteristic of the gas, rather than a continuous band of all frequencies. If the gas is made incandescent by heat or an electric discharge, the resulting spectrum is a bright-line, or emission, spectrum, consisting of a series of bright lines against a dark background. A dark-line, or absorption, spectrum is the reverse of a bright-line spectrum; it is produced when white light containing all frequencies passes through a gas not hot enough to be incandescent. It consists of a series of dark lines superimposed on a continuous spectrum, each line corresponding to a frequency where a bright line would appear if the gas were incandescent. The Fraunhofer lines appearing in the spectrum of the sun are an example of a dark-line spectrum; they are caused by the absorption of certain frequencies of light by the cooler, outer layers of the solar atmosphere. Line spectra of either type are useful in chemical analysis, since they reveal the presence of particular elements. The instrument used for studying line spectra is the spectroscope.
The explanation for exact spectral lines for each substance was provided by the quantum theory. In his 1913 model of the hydrogen atom Niels Bohr showed that the observed series of lines could be explained by assuming that electrons are restricted to atomic orbits in which their orbital angular momentum is an integral multiple of the quantity h/2π, where h is Planck's constant. The integer multiple (e.g., 1, 2, 3 …) of h/2π is usually called the quantum number and represented by the symbol n.
When an electron changes from an orbit of higher energy (higher angular momentum) to one of lower energy, a photon of light energy is emitted whose frequency ν is related to the energy difference ΔE by the equation ν=ΔE/h. For hydrogen, the frequencies of the spectral lines are given by ν=cR (1/nf2-1/ni2) where c is the speed of light, R is the Rydberg constant, and nf and ni are the final and initial quantum numbers of the electron orbits (ni is always greater than nf). The series of spectral lines for which nf=1 is known as the Lyman series; that for nf=2 is the Balmer series; that for nf=3 is the Paschen series; that for nf=4 is the Brackett series; and that for nf=5 is the Pfund series. The Bohr theory was not as successful in explaining the spectra of other substances, but later developments of the quantum theory showed that all aspects of atomic and molecular spectra can be explained quantitatively in terms of energy transitions between different allowed quantum states.
A spectrum (plural spectra or spectrums) is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by analogy to many fields other than optics. Thus, one might talk about the spectrum of political opinion, or the spectrum of activity of a drug, or the autism spectrum. In these uses, values within a spectrum may not be associated with precisely quantifiable numbers or definitions. Such uses imply a broad range of conditions or behaviors grouped together and studied under a single title for ease of discussion.
In most modern usages of spectrum there is a unifying theme between extremes at either end. Some older usages of the word did not have a unifying theme, but they led to modern ones through a sequence of events set out below. Modern usages in mathematics did evolve from a unifying theme, but this may be difficult to recognize.
In Latin spectrum means "image" or "apparition", including the meaning "spectre". 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.
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 or power as a function of frequency or wavelength, also known as a spectral density.
The term spectrum was soon applied to other waves, such as sound waves, and now applies to any signal that can be decomposed into frequency components. 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. It separates them according to its dispersion relation and a grating separates according to the grating equation and if massive particles are measured often their speed is measured. To get a spectrum, the measured function has to be transformed in their independent variable to frequencies and the dependent variable has to be reduced in regions, where the independent variable is stretched. For this imagine that the spectrum of pulse with a finite number of particles is measured on a film or a CCD. Assuming no particles are lost, any nonlinearity (compared to frequency) on the spectral separation concentrates particles at some points of the film. The same is true for taking a spectrum by scanning a monochromator with a fixed slit width. 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.