# Wavelength and refractive index relationship advice

### What is the relation between refractive index and wavelength? Spectrum-Physics - Class 10

Answer. Relation between refrective index & wavelength is v = f. Combining the above expression for velocity with the definition of index of refraction, we find a. In practice, if you want to know the relationship for a particular material between the wavelength of light and the material's refractive index, you will need to look. Given just the real part of the refractive index of the material you can't .. wavelength, but there is an integral transform relationship between the.

These are integral Hilbert-transform relationships between the real absorption per unit propagation distance and imaginary phase per unit propagation distance, i.

## Refractive index

The slashed integral stands for "Cauchy Principal Value". So, losses described by the Fresnel equations asidethere is no relationship between refractive index and transparency at a single wavelength, but there is an integral transform relationship between the two as functions of frequency - to within a constant.

The Kramers-Kronig relationships show that, given the refractive index or absorption as a function of wavelength for all wavelengths, one can work out the other to within a constant.

Below is shown a typical result of the above equations. The green curve shows a triangular absorption as a function of frequency, with frequency along the horizontal axis actually, it is gain in a Raman amplifier, but the same principle applies.

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The phase of the amplifier, proportional to an effective refractive index for our purposes, is the blue curve. This arbitrary constant is also why a single refractive index says nothing about absorption.

Footnote The KK relationships derive from stability considerations. In a passive medium, it cannot have poles in the right half plane - otherwise these would correspond to boundlessly exponentially growing waves in the output. Moreover, topological insulator material are transparent when they have nanoscale thickness.

### Wave Optics | - what is the relation between wavelength and-askIITians

These excellent properties make them a type of significant materials for infrared optics. The refractive index measures the phase velocity of light, which does not carry information.

This can occur close to resonance frequenciesfor absorbing media, in plasmasand for X-rays. In the X-ray regime the refractive indices are lower than but very close to 1 exceptions close to some resonance frequencies.

Since the refractive index of the ionosphere a plasmais less than unity, electromagnetic waves propagating through the plasma are bent "away from the normal" see Geometric optics allowing the radio wave to be refracted back toward earth, thus enabling long-distance radio communications.

See also Radio Propagation and Skywave.

### Wavelength and the Index of Refraction

Negative index metamaterials A split-ring resonator array arranged to produce a negative index of refraction for microwaves Recent research has also demonstrated the existence of materials with a negative refractive index, which can occur if permittivity and permeability have simultaneous negative values. The resulting negative refraction i. Ewald—Oseen extinction theorem At the atomic scale, an electromagnetic wave's phase velocity is slowed in a material because the electric field creates a disturbance in the charges of each atom primarily the electrons proportional to the electric susceptibility of the medium.

Similarly, the magnetic field creates a disturbance proportional to the magnetic susceptibility.

As the electromagnetic fields oscillate in the wave, the charges in the material will be "shaken" back and forth at the same frequency.

The light wave traveling in the medium is the macroscopic superposition sum of all such contributions in the material: This wave is typically a wave with the same frequency but shorter wavelength than the original, leading to a slowing of the wave's phase velocity.

Most of the radiation from oscillating material charges will modify the incoming wave, changing its velocity.

However, some net energy will be radiated in other directions or even at other frequencies see scattering. Depending on the relative phase of the original driving wave and the waves radiated by the charge motion, there are several possibilities: This is the normal refraction of transparent materials like glass or water, and corresponds to a refractive index which is real and greater than 1. This is called "anomalous refraction", and is observed close to absorption lines typically in infrared spectrawith X-rays in ordinary materials, and with radio waves in Earth's ionosphere.

It corresponds to a permittivity less than 1, which causes the refractive index to be also less than unity and the phase velocity of light greater than the speed of light in vacuum c note that the signal velocity is still less than c, as discussed above.