Physical Terms and Definitions

Optical spectrum


Optical spectrum

The optical spectrum (light or visible spectrum) is the portion of the electromagnetic spectrum that is visible to the human eye. There are no exact bounds to the optical spectrum; a typical human eye will respond to wavelengths from 400 to 700 nm, although some people may be able to perceive wavelengths from 380 to 780 nm. A light-adapted eye typically has its maximum sensitivity at ~555 nm, in the yellow region of the optical spectrum.

Wavelengths visible to the eye are defined by the spectral range of the "optical window", the region of the electromagnetic spectrum which passes largely unattenuated through the Earth's atmosphere (although blue light is scattered more than red light, which is the reason the sky is blue). Electromagnetic radiation outside the optical wavelength range is almost entirely absorbed by the atmosphere.

Historical use of the term

Sir Isaac Newton first used the word spectrum in 1666 to refer to the celebrated Phenomenon of Colours in which he demonstrated that "white light" was actually made up of a spectrum of colors. He refracted "white light" by projecting a slit of sunlight into a glass prism.

Prism showing the spectrum of colors which make up "white light".

It is possible to simulate his discovery with a slit or spot of "white light" projected onto a triangular prism. It will refract the differing wavelengths at different angles/speeds, resulting in a projected spectrum of the light's constituent colors. This is because the glass of which the prism is made is a dispersive medium. It's triangular shape allows the longer (red) wavelengths to pass through first, then the green, then the blue. Blue is the higher frequency color, so it stays in the prism longer, and bends and exits the prism at the steepest angle than the red or green in the prism. The resulting image is a saturated spectrum or rainbow of colored lights projected on the wall.


Coherent waves (monochromatic)

Incoherent waves of the same frequency (monochromatic)

Incoherent waves with different frequencies (not monochromatic)

Coherence is a property of waves that measures the ability of the waves to interfere with each other. Two waves that are coherent can be combined to produce an unmoving distribution of constructive and destructive interference (a visible interference pattern) depending on the relative phase of the waves at their meeting point. Waves that are incoherent, when combined, produce rapidly moving areas of constructive and destructive interference and therefore do not produce a visible interference pattern.
A wave can also be coherent with itself, a property known as temporal coherence. If a wave is combined with a delayed copy of itself (as in a Michelson interferometer), the duration of the delay over which it produces visible interference is known as the coherence time of the wave, Δtc. From this, a corresponding coherence length can be calculated:

where c is the speed of the wave.

The temporal coherence of a wave is related to the spectral bandwidth of the source. A truly monochromatic (single frequency) wave would have an infinite coherence time and length. In practice, no wave is truly monochromatic (since this requires a wavetrain of infinite duration), but in general, the coherence time of the source is inversely proportional to its bandwidth.
Waves also have the related property of spatial coherence; this is the ability of any one spatial position of the wavefront to interfer with any other spatial position. Young's double-slit experiment relies on spatial coherence of the beam illuminating the two slits; if the beam was spatially incoherent, i.e. if the sunlight was not first passed through a single slit, then no interference pattern would be seen.
Spatial coherence is high for sphere waves and plane waves, and therefore is related to the size of the light source. A point source of zero diameter emits spatially coherent light, while the light from a collection of point-sources (or from a source of finite diameter) would have lower coherence. Spatial coherence can be increased with a spatial filter; a very small pinhole preceded by a condenser lens. The spatial coherence of light will increase as it travels away from the source and becomes more like a sphere or plane wave. Light from distant stars, though far from monochromatic, has extremely high spatial coherence. The science of stellar interferometry relies on the coherence of starlight.
Light waves produced by a laser often have high temporal and spatial coherence (though the degree of coherence depends strongly on the exact properties of the laser). For example, a stabilised helium-neon laser can produce light with coherence lengths in excess of 5 m. Light from common sources (such as light bulbs) is not monochromatic and has a very short coherence length (~1 μm), and can be considered totally temporally incoherent for most purposes. Spatial coherence of laser beams also manifests itself as speckle patterns and diffraction fringes seen at the edges of shadow.


Something which is monochromatic has a single color. In physics, the word is used more specifically to refer to electromagnetic radiation of a single wavelength.
For an image, the term monochrome is essentially the same as black-and-white, but the monochrome may be preferred to indicate that combinations such as green-and-white, green-and-black, etc., are not excluded.
In computing, monochrome has two meanings: it can mean having only one color which is either on or off, or also allowing shades of that color. Thus it has the same ambiguity as the term black-and-white.
A monochrome computer display is capable of displaying only a single color, often green, amber, red or white, and often also shades of that color.
In the physical sense, no real source of electromagnetic radiation is purely monochromatic, since that would require a wave of infinite duration. Even sources such as lasers have some narrow range of wavelengths (known as the linewidth or bandwidth of the source) over which they operate.
The word monochromatic comes from the two Greek words mono (meaning "one"), and chroma (χρωμα, meaning "surface" or "the color of the skin").


In electrodynamics, polarization is a property of waves, such as light and other electromagnetic radiation. Unlike more familiar wave phenomena such as waves on water or sound waves, electromagnetic waves are three-dimensional, and it is their vector nature that gives rise to the phenomenon of polarization.

Plane waves

The simplest manifestation of polarization to visualize is that of a plane wave, which is a good approximation to most light waves. A plane wave is one where the direction of the magnetic and electric fields are confined to a plane perpendicular to the propagation direction. Simply because the plane is two-dimensional, the electric vector in the plane at a point in space can be decomposed into two orthogonal components. Call these the x and y components (following the conventions of analytic geometry). For a simple harmonic wave, where the amplitude of the electric vector varies in a sinusoidal manner, the two components have exactly the same frequency. However, these components have two other defining characteristics that can differ. First, the two components may not have the same amplitude. Second, the two components may not have the same phase, that is they may not reach their maxima and minima at the same time in the fixed plane we are talking about. By considering the shape traced out in a fixed plane by the electric vector as such a plane wave passes over it (a Lissajous figure), we obtain a description of the polarization state. The following figures show some examples of the evolution of the electric field vector (blue) with time, along with its x and y components (red/left and green/right) and the path made by the vector in the plane (purple):

Linear Circular Elliptical

Consider first the special case (left) where the two orthogonal components are in phase. In this case the strength of the two components are always equal or related by a constant ratio, so the direction of the electric vector (the vector sum of these two components) will always fall on a single line in the plane. We call this special case linear polarization. The direction of this line will depend on the relative amplitude of the two components. This direction can be in any angle in the plane, but the direction never varies.
Now consider another special case (center), where the two orthogonal components have exactly the same amplitude and are exactly ninety degrees out of phase. In this case one component is zero when the other component is at maximum or minimum amplitude. Notice that there are two possible phase relationships that satisfy this requirement. The x component can be ninety degrees ahead of the y component or it can be ninety degrees behind the y component. In this special case the electric vector in the plane formed by summing the two components will rotate in a circle. We call this special case circular polarization. The direction of rotation will depend on which of the two phase relationships exists. We call these cases right-hand circular polarization and left-hand circular polarization, depending on which way the electric vector rotates.
All the other cases, that is where the two components are not in phase and either do not have the same amplitude and/or are not ninety degrees out of phase (e.g. right) are called elliptical polarization because the sum electric vector in the plane will trace out an ellipse (the "polarization ellipse").

Incoherent radiation

In nature, electromagnetic radiation is often produced by a large ensemble of individual radiators, producing waves independently of each other. This type of light is termed incoherent. In general there is no single frequency but rather a spectrum of different frequencies present, and even if filtered to an arbitrarily narrow frequency range, there may not be a consistent state of polarization. However, this does not mean that polarization is only a feature of coherent radiation. Incoherent radiation may show statistical correlation between the components of the electric field, which can be interpreted as partial polarization. In general it is possible to describe an observed wave field as the sum of a completely incoherent part (no correlations) and a completely polarized part. One may then describe the light in terms of the degree of polarization, and the parameters of the polarization ellipse.

Observing polarization effects in everyday life

All light which reflects off a flat surface is polarized. You can take a polarizing filter and hold it at 90 degrees to the reflection, and it will be gone. Polarizing filters remove light propogating at 90 degrees to the filter. This is why you can take 2 polarizers and lay them atop one another at 90 degree angles to each other and no light will pass through.
Polarized light can be observed all around you if you know what it is and what to look for. (the lenses of Polaroid® sunglasses will work to demonstrate). While viewing through the filter, rotate it, and if linear or elliptically polarized light is present the degree of illumination will change. Polarization by scattering is observed as light passes through our atmosphere. The scattered light often produces a glare in the skies. Photographers know that this partial polarization of scattered light produces a washed-out sky. An easy first phenomenon to observe is at sunset to view the horizon at a 90° angle from the sunset. Another easily observed effect is the drastic reduction in brightness of images of the sky and clouds reflected from horizontal surfaces, which is the reason why polarizing filters are often used in sunglasses. Also frequently visible through polarizing sunglasses are rainbow-like patterns caused by color-dependent birefringent effects, for example in toughened glass (e.g. car windows) or items made from transparent plastics. The role played by polarization in the operation of liquid crystal displays (LCDs) is also frequently apparent to the wearer of polarizing sunglasses, which may reduce the contrast or even make the display unreadable.
In fact, the naked human eye is weakly sensitive to polarization, without the need for intervening filters.

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