A report on Wavelength and Refractive index

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.

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

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.

$Refraction of a light ray$

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

$Thomas Young coined the term index of refraction.$

Wavelength is decreased in a medium with slower propagation.

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

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

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

Separation of colors by a prism (click for animation)

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

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

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

A sinusoidal wave travelling in a nonuniform medium, with loss

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

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

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

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.

Wavelength of a periodic but non-sinusoidal waveform.

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

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

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.

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

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

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

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

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

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.

- Refractive index

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

- Wavelength

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

Refraction

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

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

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

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.

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

For light, refraction follows Snell's law, which states that, for a given pair of media, the ratio of the sines of the angle of incidence θ1 and angle of refraction θ2 is equal to the ratio of phase velocities (v1 / v2) in the two media, or equivalently, to the refractive indices (n2 / n1) of the two media.

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

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

Dispersion (optics)

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Phenomenon in which the phase velocity of a wave depends on its frequency; sometimes the term chromatic dispersion is used for specificity to optics in particular.

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

A compact fluorescent lamp seen through an Amici prism

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

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).

Most often, chromatic dispersion refers to bulk material dispersion, that is, the change in refractive index with optical frequency.

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 typically include a core surrounded by a transparent cladding material with a lower index of refraction.

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.

Light

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Electromagnetic radiation within the portion of the electromagnetic spectrum that is perceived by the human eye.

The electromagnetic spectrum, with the visible portion highlighted

Beam of sun light inside the cavity of Rocca ill'Abissu at Fondachelli-Fantina, Sicily

$Due to refraction, the straw dipped in water appears bent and the ruler scale compressed when viewed from a shallow angle.$

Hong Kong illuminated by colourful artificial lighting.

$Thomas Young's sketch of a double-slit experiment showing diffraction. Young's experiments supported the theory that light consists of waves.$

Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 terahertz, between the infrared (with longer wavelengths) and the ultraviolet (with shorter wavelengths).

where θ1 is the angle between the ray and the surface normal in the first medium, θ2 is the angle between the ray and the surface normal in the second medium and n1 and n2 are the indices of refraction, n = 1 in a vacuum and n > 1 in a transparent substance.

Simple ray diagram showing typical chief and marginal rays

Numerical aperture

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[[Image:Numerical aperture.svg|thumb|The numerical aperture with respect to a point

By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another, provided there is no refractive power at the interface.

is the wavelength of the light.

Wave

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Propagating dynamic disturbance of one or more quantities.

Example of biological waves expanding over the brain cortex, an example of spreading depolarizations.

Wavelength λ, can be measured between any two corresponding points on a waveform

Animation of two waves, the green wave moves to the right while blue wave moves to the left, the net red wave amplitude at each point is the sum of the amplitudes of the individual waves. Note that f(x,t) + g(x,t) = u(x,t)

Sine, square, triangle and sawtooth waveforms.

Amplitude modulation can be achieved through f(x,t) = 1.00×sin(2π/0.10×(x−1.00×t)) and g(x,t) = 1.00×sin(2π/0.11×(x−1.00×t))only the resultant is visible to improve clarity of waveform.

Illustration of the envelope (the slowly varying red curve) of an amplitude-modulated wave. The fast varying blue curve is the carrier wave, which is being modulated.

The red square moves with the phase velocity, while the green circles propagate with the group velocity

A wave with the group and phase velocities going in different directions

Standing wave. The red dots represent the wave nodes

$Light beam exhibiting reflection, refraction, transmission and dispersion when encountering a prism$

$Sinusoidal traveling plane wave entering a region of lower wave velocity at an angle, illustrating the decrease in wavelength and change of direction (refraction) that results.$

Identical waves from two sources undergoing interference. Observed at the bottom one sees 5 positions where the waves add in phase, but in between which they are out of phase and cancel.

Schematic of light being dispersed by a prism. Click to see animation.

A propagating wave packet; in general, the envelope of the wave packet moves at a different speed than the constituent waves.

Animation showing the effect of a cross-polarized gravitational wave on a ring of test particles

One-dimensional standing waves; the fundamental mode and the first 5 overtones.

A two-dimensional standing wave on a disk; this is the fundamental mode.

A standing wave on a disk with two nodal lines crossing at the center; this is an overtone.

Electromagnetic waves, according to their frequencies (or wavelengths) have more specific designations including radio waves, infrared radiation, terahertz waves, visible light, ultraviolet radiation, X-rays and gamma rays.

A material which absorbs a wave's energy, either in transmission or reflection, is characterized by a refractive index which is complex.

$The binocular microscope is a conventional optical system. Spatial resolution is confined by a diffraction limit that is a little above 200 nanometers.$

Superlens

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Lens which uses metamaterials to go beyond the diffraction limit.

$The binocular microscope is a conventional optical system. Spatial resolution is confined by a diffraction limit that is a little above 200 nanometers.$

Schematic depictions and images of commonly used metallic nanoprobes that can be used to see a sample in nanometer resolution. Notice that the tips of the three nanoprobes are 100 nanometers.

DVD (digital versatile disc). A laser is employed for data transfer.

The "Electrocomposeur" was an electron-beam lithography machine (electron microscope) designed for mask writing. It was developed in the early 1970s and deployed in the mid 1970s.

A prism composed of high performance Swiss rolls which behaves as a magnetic faceplate, transferring a magnetic field distribution faithfully from the input to the output face.

Furthermore, the level of feature detail, or image resolution, is limited to a length of a wave of radiation.

Microscopy takes into account parameters such as lens aperture, distance from the object to the lens, and the refractive index of the observed material.

$A diffraction pattern of a red laser beam projected onto a plate after passing through a small circular aperture in another plate$

Diffraction

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Obstacle or opening.

$A diffraction pattern of a red laser beam projected onto a plate after passing through a small circular aperture in another plate$

Infinitely many points (three shown) along length d project phase contributions from the wavefront, producing a continuously varying intensity θ on the registering plate.

$Thomas Young's sketch of two-slit diffraction for water waves, which he presented to the Royal Society in 1803.$

$Photograph of single-slit diffraction in a circular ripple tank$

$Circular waves generated by diffraction from the narrow entrance of a flooded coastal quarry$

$A solar glory on steam from hot springs. A glory is an optical phenomenon produced by light backscattered (a combination of diffraction, reflection and refraction) towards its source by a cloud of uniformly sized water droplets.$

$2D Single-slit diffraction with width changing animation$

$Numerical approximation of diffraction pattern from a slit of width four wavelengths with an incident plane wave. The main central beam, nulls, and phase reversals are apparent.$

$Graph and image of single-slit diffraction.$

$2-slit (top) and 5-slit diffraction of red laser light$

$Diffraction of a red laser using a diffraction grating.$

$A diffraction pattern of a 633 nm laser through a grid of 150 slits$

A computer-generated image of an Airy disk.

$Computer generated light diffraction pattern from a circular aperture of diameter 0.5 micrometre at a wavelength of 0.6 micrometre (red-light) at distances of 0.1 cm – 1 cm in steps of 0.1 cm. One can see the image moving from the Fresnel region into the Fraunhofer region where the Airy pattern is seen.$

The Airy disk around each of the stars from the 2.56 m telescope aperture can be seen in this lucky image of the binary star zeta Boötis.

$The upper half of this image shows a diffraction pattern of He-Ne laser beam on an elliptic aperture. The lower half is its 2D Fourier transform approximately reconstructing the shape of the aperture.$

$Following Bragg's law, each dot (or reflection) in this diffraction pattern forms from the constructive interference of X-rays passing through a crystal. The data can be used to determine the crystal's atomic structure.$

$Computer generated intensity pattern formed on a screen by diffraction from a square aperture.$

$Generation of an interference pattern from two-slit diffraction.$

$Computational model of an interference pattern from two-slit diffraction.$

$Optical diffraction pattern ( laser), (analogous to X-ray crystallography)$

$Colors seen in a spider web are partially due to diffraction, according to some analyses.<ref>{{cite web|url = http://www.itp.uni-hannover.de/%7Ezawischa/ITP/spiderweb.html|title = Optical effects on spider webs|author = Dietrich Zawischa|access-date = 2007-09-21}}</ref>$

$Diffraction on a sharp metallic edge$

$Diffraction on a soft aperture, with a gradient of conductivity over the image width$

The characteristic bending pattern is most pronounced when a wave from a coherent source (such as a laser) encounters a slit/aperture that is comparable in size to its wavelength, as shown in the inserted image.

These effects also occur when a light wave travels through a medium with a varying refractive index, or when a sound wave travels through a medium with varying acoustic impedance – all waves diffract, including gravitational waves, water waves, and other electromagnetic waves such as X-rays and radio waves.