# Refractive index and frequency relationship

### Index of refraction related to wavelength & frequency | Physics Forums

In optics, the refractive index or index of refraction of a material is a dimensionless number that This implies that vacuum has a refractive index of 1 , and that the frequency (f = v/λ) of the wave is .. For a more accurate description of the wavelength dependence of the refractive index, the Sellmeier equation can be used. Calculate critical angle given refractive index. The frequency of light does not change as it refracts. When you use this relationship, angle \theta _{1}. Wavelength and the Index of Refraction In the above equation, the frequencies cancel because frequency does not change as light moves from one medium.

### The Feynman Lectures on Physics Vol. I Ch. The Origin of the Refractive Index

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. 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.

## Refractive index

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.

Nor can it have zeros anywhere: Under these conditions, it follows immediately that the real part must define the imaginary part, modulo a constant, and contrariwise. However, some net energy will be radiated in other directions or even at other frequencies see scattering.

## Refraction of light

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.

If the response is sufficiently strong and out-of-phase, the result is a negative value of permittivity and imaginary index of refraction, as observed in metals or plasma. This is light absorption in opaque materials and corresponds to an imaginary refractive index. If the electrons emit a light wave which is in phase with the light wave shaking them, it will amplify the light wave. This is rare, but occurs in lasers due to stimulated emission. It corresponds to an imaginary index of refraction, with the opposite sign to that of absorption.

- Index of refraction related to wavelength & frequency

Dispersion[ edit ] 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. Dispersion optics The refractive index of materials varies with the wavelength and frequency of light. Dispersion also causes the focal length of lenses to be wavelength dependent. This is a type of chromatic aberrationwhich often needs to be corrected for in imaging systems.

In regions of the spectrum where the material does not absorb light, the refractive index tends to decrease with increasing wavelength, and thus increase with frequency. This is called "normal dispersion", in contrast to "anomalous dispersion", where the refractive index increases with wavelength. For optics in the visual range, the amount of dispersion of a lens material is often quantified by the Abbe number: