Rayleigh Scattering


Rayleigh scattering – scattering of light by particles that are less than 1/15 of the wavelength of the light.  Atoms and ordinary molecules which have a diameter of less than one nanometer are included in Rayleigh scattering. 

-  When light travels through a medium, it interacts with the medium and this causes the scattering of light.

-  Photons are absorbed by molecules in the medium, and this causes the molecules to vibrate and then re-emit the photons.  When the photons are re-emitted, they have the same frequency and wavelength, but are re-emitted in random directions.

-  There are a large number of photons interacting with the molecules, and so photons are emitted from molecules in all directions and appear to be “spherical wavelets” of light. 

-  The scattering of light increases with frequency.  Therefore light with higher frequencies undergoes more lateral scattering than light with lower frequencies.  

-  In dense, uniform substances, there is little lateral scattering, and the denser the substance, the less lateral scattering. 

-  In media with random, widely spaced molecules, the light is scattered randomly in all directions except for the direction that the incident light was traveling.  Therefore, lateral scattering is possible and observable.

  -  In dense, uniform media, scattered light will interfere constructively in the forward direction, but interfere destructively in all other directions.  Therefore, little or no lateral scattering will be observed. 


Index of Refraction (n):  When light is transmitted through a material, each photon travels at the speed of light, c.  However, Rayleigh scattering causes the transmitted wave to be out of phase with the free-space (initial) wave.  The light is scattered many times as it travels through the medium.  Each time the light is scattered, the scattering causes a phase shift.  This translates to a change in the phase velocity within the medium, of the beam from c.  Therefore, there is an index of refraction for homogeneous materials, n = c/v. 


-         When the light is scattered, the “wavelets” interfere constructively in the forward direction and form the secondary wave front.

-         The superposition of the primary and secondary wave front (both traveling at speed c) is the transmitted wave. 

-         At low frequencies, the molecules are able to vibrate almost in phase with the light.  However, as the frequency increases, the vibration of the molecules lag behind, and the phase lag increases with increased frequency .

o       At resonance, wo, the phase lag is 90 degrees.  As the frequency increases, the phase lag increases to 180 degrees.


-         The superposition of the primary and secondary waves make up the transmitted wave.  If the secondary wave is phase shifted from the primary wave, the transmitted wave is phase shifted from the primary wave (or free-space wave) as well.

-         As the transmitted wave continues to travel through the material, scattering continues to occur causing a greater phase lag or phase lead.  These changes in phase correspond to changes in speed of the wave traveling through the material. 

o       At frequencies less than wo, the transmitted wave lags the free-space wave.  This corresponds to a speed v<c for the transmitted wave and an index of refraction, n>1.

o       At frequencies above wo, the transmitted wave leads the free-space wave.  This corresponds to a speed v>c and an index of refraction, n<1. 

o       At the frequency wo, the phase lag is 180 degrees, therefore there is no phase shift, v=c and n=1. 


The Blue Sky: 

Rayleigh scattering increases with frequency.  Therefore, blue light is scattered more than red light.  When light from the sun interacts with our atmosphere, the lateral scattering of blue light is much greater than the lateral scattering of the rest of the visible spectrum, and this is partly why the sky appears blue. 



Hecht, Eugene.  Optics.  Addison Wesley: San Francisco, 2002.

Rayleigh Scattering from Wikipedia.  Retrieved April 21, 2003 from http://www.wikipedia.org/wiki/Rayleigh_scattering