A report on Wavelength and Dispersion (optics)

The wavelength of a sine wave, λ, can be measured between any two points with the same phase, such as between crests (on top), or troughs (on bottom), or corresponding zero crossings as shown.

$In a dispersive prism, material dispersion (a wavelength-dependent refractive index) causes different colors to refract at different angles, splitting white light into a spectrum.$

Sinusoidal standing waves in a box that constrains the end points to be nodes will have an integer number of half wavelengths fitting in the box.

A compact fluorescent lamp seen through an Amici prism

A standing wave (black) depicted as the sum of two propagating waves traveling in opposite directions (red and blue)

$The variation of refractive index vs. vacuum wavelength for various glasses. The wavelengths of visible light are shaded in grey.$

Wavelength is decreased in a medium with slower propagation.

$Refraction: upon entering a medium where its speed is lower, the wave changes direction.$

Separation of colors by a prism (click for animation)

Various local wavelengths on a crest-to-crest basis in an ocean wave approaching shore

A sinusoidal wave travelling in a nonuniform medium, with loss

A wave on a line of atoms can be interpreted according to a variety of wavelengths.

Wavelength of a periodic but non-sinusoidal waveform.

Pattern of light intensity on a screen for light passing through two slits. The labels on the right refer to the difference of the path lengths from the two slits, which are idealized here as point sources.

$Diffraction pattern of a double slit has a single-slit envelope.$

Relationship between wavelength, angular wavelength, and other wave properties.

The most familiar example of dispersion is probably a rainbow, in which dispersion causes the spatial separation of a white light into components of different wavelengths (different colors).

- Dispersion (optics)

In a dispersive medium, the phase speed itself depends upon the frequency of the wave, making the relationship between wavelength and frequency nonlinear.

- Wavelength

4 related topics with Alpha

$A ray of light being refracted in a plastic block.$

Refraction

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Redirection of a wave as it passes from one medium to another.

$A ray of light being refracted in a plastic block.$

$Refraction of light at the interface between two media of different refractive indices, with n2 > n1. Since the phase velocity is lower in the second medium (v2 < v1), the angle of refraction θ2 is less than the angle of incidence θ1; that is, the ray in the higher-index medium is closer to the normal.$

$A pen partially submerged in a bowl of water appears bent due to refraction at the water surface.$

When a wave moves into a slower medium the wavefronts get compressed. For the wavefronts to stay connected at the boundary the wave must change direction.

$A pencil part immersed in water looks bent due to refraction: the light waves from X change direction and so seem to originate at Y.$

$An image of the Golden Gate Bridge is refracted and bent by many differing three-dimensional drops of water.$

$The sun appears slightly flattened when close to the horizon due to refraction in the atmosphere.$

Heat haze in the engine exhaust above a diesel locomotive.

$Water waves are almost parallel to the beach when they hit it because they gradually refract towards land as the water gets shallower.$

The refractive index of materials varies with the wavelength of light, and thus the angle of the refraction also varies correspondingly.

This is called dispersion and causes prisms and rainbows to divide white light into its constituent spectral colors.

$A ray of light being refracted in a plastic block$

Refractive index

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Optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.

$A ray of light being refracted in a plastic block$

$Refraction of a light ray$

$Thomas Young coined the term index of refraction.$

$Diamonds have a very high refractive index of 2.417.$

$A split-ring resonator array arranged to produce a negative index of refraction for microwaves$

$In optical mineralogy, thin sections are used to study rocks. The method is based on the distinct refractive indices of different minerals.$

$Light of different colors has slightly different refractive indices in water and therefore shows up at different positions in the rainbow.$

$In a prism, dispersion causes different colors to refract at different angles, splitting white light into a rainbow of colors.$

$The variation of refractive index with wavelength for various glasses. The shaded zone indicates the range of visible light.$

The colors of a soap bubble are determined by the optical path length through the thin soap film in a phenomenon called thin-film interference.

Total internal reflection can be seen at the air-water boundary.

$The power of a magnifying glass is determined by the shape and refractive index of the lens.$

$The relation between the refractive index and the density of silicate and borosilicate glasses$

$A calcite crystal laid upon a paper with some letters showing double refraction$

Birefringent materials can give rise to colors when placed between crossed polarizers. This is the basis for photoelasticity.

$A gradient-index lens with a parabolic variation of refractive index (n) with radial distance (x). The lens focuses light in the same way as a conventional lens.$

$The principle of many refractometers$

$A handheld refractometer used to measure the sugar content of fruits$

A differential interference contrast microscopy image of yeast cells

The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/n, and similarly the wavelength in that medium is λ = λ0/n, where λ0 is the wavelength of that light in vacuum.

This is called dispersion.

Electromagnetic radiation

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In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, propagating through space, carrying electromagnetic radiant energy.

Shows the relative wavelengths of the electromagnetic waves of three different colours of light (blue, green, and red) with a distance scale in micrometers along the x-axis.

In electromagnetic radiation (such as microwaves from an antenna, shown here) the term "radiation" applies only to the parts of the electromagnetic field that radiate into infinite space and decrease in intensity by an inverse-square law of power, so that the total radiation energy that crosses through an imaginary spherical surface is the same, no matter how far away from the antenna the spherical surface is drawn. Electromagnetic radiation thus includes the far field part of the electromagnetic field around a transmitter. A part of the "near-field" close to the transmitter, forms part of the changing electromagnetic field, but does not count as electromagnetic radiation.

Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This 3D animation shows a plane linearly polarized wave propagating from left to right. The electric and magnetic fields in such a wave are in-phase with each other, reaching minima and maxima together.

Representation of the electric field vector of a wave of circularly polarized electromagnetic radiation.

Electromagnetic spectrum with visible light highlighted

Rough plot of Earth's atmospheric absorption and scattering (or opacity) of various wavelengths of electromagnetic radiation

The position of an electromagnetic wave within the electromagnetic spectrum can be characterized by either its frequency of oscillation or its wavelength.

Light of composite wavelengths (natural sunlight) disperses into a visible spectrum passing through a prism, because of the wavelength-dependent refractive index of the prism material (dispersion); that is, each component wave within the composite light is bent a different amount.

Optical fiber

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Flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair.

Fiber crew installing a 432-count fiber cable underneath the streets of Midtown Manhattan, New York City

A TOSLINK fiber optic audio cable with red light being shone in one end transmits the light to the other end

A wall-mount cabinet containing optical fiber interconnects. The yellow cables are single mode fibers; the orange and aqua cables are multi-mode fibers: 50/125 µm OM2 and 50/125 µm OM3 fibers respectively.

Daniel Colladon first described this "light fountain" or "light pipe" in an 1842 article titled "On the reflections of a ray of light inside a parabolic liquid stream". This particular illustration comes from a later article by Colladon, in 1884.

Light reflected from optical fiber illuminates exhibited model

Use of optical fiber in a decorative lamp or nightlight

The propagation of light through a multi-mode optical fiber.

A laser bouncing down an acrylic rod, illustrating the total internal reflection of light in a multi-mode optical fiber.

Experimental attenuation curve of low loss multimode silica and ZBLAN fiber. Black triangle points and gray arrows illustrate a four order of magnitude reduction in the attenuation of silica optical fibers over four decades from ~1000 dB/km in 1965 to ~0.17 dB/km in 2005.

Theoretical loss spectra (attenuation, dB/km) for Silica optical fiber (dashed blue line) and typical ZBLAN optical fiber (solid gray line) as function of wavelength (microns).

The P4O10 cagelike structure—the basic building block for phosphate glass

Illustration of the modified chemical vapor deposition (inside) process

Cross-section of a fiber drawn from a D-shaped preform

An aerial optical fiber splice enclosure lowered during installation. The individual fibers are fused together and stored within the enclosure for protection from damage

Optical fibers can be used as sensors to measure strain, temperature, pressure, and other quantities by modifying a fiber so that the property being measured modulates the intensity, phase, polarization, wavelength, or transit time of light in the fiber.

However, this high numerical aperture increases the amount of dispersion as rays at different angles have different path lengths and therefore take different amounts of time to traverse the fiber.