# Relationship refractive index permittivity and permeability

### Dielectrics and Optics

The refractive index of a material, n, is defined as the ratio of the speed of light this time in terms of the electric permittivity (ε) and magnetic permeability (μ) of. in relating the index of refraction to the relative permittivity (dielectric constant/ function). it is known that n = \sqrt{\epsilon_r} for optical. Loght is an electromagnetic wave, and Maxwell showed that light [math]c[/math] travels at the EM velocity [math]U/\sqrt{\epsilon\mu}[/math]. SI sets U=1, but in.

What do we know about the three beams? The incident beam is characterized by its wavelength li, its frequency ni and its velocity c0, the direction of its polarization in some coordinate system of our choice, and the arbitrary angle of incidence a.

We know, it is hoped, the simple dispersion relation for vacuum. The incident beam also has a certain amplitude of the electric field and of the magnetic field, of course which we call E0.

## Relative Permittivity and Refractive Index

The intensity Ii of the light that the incident beams embodies, i. The reflected beam follows one of the basic laws of optics, i.

What we do not know is its amplitude and its polarization, and these two quantities must somehow depend on the properties of the incident beam and the properties of the dielectric. If we now consider the refracted beam, we know that it travels under an angle b, has the same frequency as the incident beam, but a wavelength ld and a velocity c that is different from li and c0. Moreover, we must expect that it is damped or attenuated, i.

All parameters of the refracted beam may depend on the polarization of the incident beam.

### Relative Permittivity and Refractive Index | Physics Forums

Againbasic optics teaches that there are some simple relations. 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.

## Refractive index

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.

**Lec 18: Boundary Conditions for Dielectrics - 8.03 Vibrations and Waves, Fall 2004 (Walter Lewin)**

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. 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.

### DoITPoMS - TLP Library Dielectric materials - The dielectric constant and the refractive index

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: