Light in different media II

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Light in different media II

Dispersion, phase and group velocity,



A short review

• Polarization of light

Linear vertical

Linear 45°

Eliptical Different polarization of light get reflected and refracted with different amplitudes


A short review

Malus’s law, polarized light

passing through an analyzer






In Out Material with an index of

refraction n

The light slows down inside the material, therefore its wavelength becomes shorter and its phase gets shifted

) /

sin( nx t A



A short review


A short review

Scattering: The process whereby EM radiation is absorbed and immediately

re-emitted by a particle or molecule – energy can be emitted in multiple-directions

• Rayleigh: Occurs when the wavelength >> the particle size, scattering occurs at a molecular level,

• Mie: Occurs when the wavelength ≅ particle size, Explains scattering around larger droplets such as Corona around the sun or moon, Glory and similar phenomena.





• The dependence of wave speed and index of refraction on wavelength is called dispersion,

• The index of refraction depends on the frequency of the light: the higher the frequency, the higher the index of refraction,

• Because white light is a mixture of

frequencies, different wavelengths

travel in different directions.



• Dispersion is the cause of chromatic aberration in a simple lens:

• Different colours focus at different points,

• It’s a common defect of simple lenses,

• Sometimes you see a fringe of colours around an image seen through a lens or a telescope,

• Chromatic aberration can be corrected by combining two or more


White light



• 1665-1666 – First experiment of Isaac Newton with dispersion,

• For this distribution of colours Newton coined the term




• The experimentum crucis

• White light can be dispersed into different wavelengths,

• Dispersed ray (monochromatic) cannot be divided into other wavelengths

Slit Slit



• White light is a ―Heterogeneous mixture of different refrangible Rays‖

• Colours of the spectrum cannot be individually modified.

• Colours are ―Original and connate properties, which in divers Rays are divers. Some Rays are disposed to exhibit a red colour and no other; some a yellow and no other, some a green and no other, and so of the rest‖.

Newton’s conclusions



• In the presence of dispersion, wave velocity is no longer uniquely defined, giving rise to the distinction of phase velocity and group velocity.

• A well-known effect of phase velocity dispersion is the color dependence of light refraction that can be observed in prisms and rainbows.

• Dispersion may be caused either by geometric boundary conditions (waveguides, shallow water) or by interaction of the waves with the transmitting medium.



• is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the

group velocity depends on the frequency.

• Media having such a property are termed dispersive media. Dispersion is sometimes called chromatic dispersion to emphasize its wavelength-dependent nature, or group-velocity dispersion (GVD) to

emphasize the role of the group velocity.



Refractive index (n)

The maximum of

absorption can be at the same range as anormal dispersion,

It can cause that the

medium is opaque in this range.

• Dispersion is called normal when the refractive index decreases with the wavelength,

• For materials with selective absorption the refractive index can increase in some selective wavelength ranges…

• This kind of dispersion is called anomalous.


Dispersion - Rainbow

• A rainbow is caused by the dispersion of light in droplets of rain.

When sunlight enters a drop, it is separated into its coloured components.

• The final direction of light is quite opposite to its

incident direction.

• Violet light changes its direction by 320°.

• Red light changes its direction by 318°.


Phase and group velocity


Wave velocity in dispersive media

• In a range of absorption maximum, the refractive index can be even <1,

it means that for 0<n<1 the wave speed:

• There is no paradox in it.

• Phase velocity is the rate at which the phase of the wave propagates,

• It this does not indicate any

superluminal information or energy transfer,

Phase velocity


Phase velocity

• In a dispersive medium, the phase velocity varies with frequency and is not necessarily the same as the group velocity of the wave, which is the rate at which changes in amplitude (known as the

envelope of the wave) propagate.

• In some specific cases the phase velocity has a negative sign as group velocity.

moves with the phase velocity, moves with the group velocity


Group velocity

• The group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or

envelope of the wave — propagates through space.

• The group velocity is often thought of as the velocity at which energy or information is conveyed along a wave.

• In most cases this is accurate, and the group velocity can be thought of as the signal velocity of the waveform.

• However, if the wave is travelling through an absorptive medium, this does not always hold.


Group velocity

• various experiments have verified that it is possible for the group velocity of laser light pulses sent through specially prepared materials to significantly exceed the speed of light in vacuum,

• However, superluminal communication is not possible in this case, since the signal velocity remains less than the speed of light.

• It is also possible to reduce the group velocity to zero, stopping the pulse, or have negative group velocity, making the pulse appear to propagate


• However, in all these cases, photons continue to propagate at the expected speed of light in the medium

• 1999 Rowland Institute for Science, Cambridge,

• 2000 NEC Research Institute, Princton,

Group velocity (equal to an electron's speed) should not be confused with phase velocity (equal to the product of the electron's frequency multiplied by its





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