A Guide to Mie Scattering

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Mie scattering is the elastic scattered light of particles with a diameter larger than or equal to the wavelength of incident light, and the theory is a lot simpler than people think. However, to fully understand Mie scattering and how it affects our view of the world, we must first look at Rayleigh scattering.

Rayleigh Scattering

When compared to Mie scattering we are able to understand both with greater ease. Rayleigh scattering is the scattering of light off molecules in the air. It can be extended to light particles scattering up to approximately a tenth of the wavelength of light. This ‘Rayleigh’ scattering of the air molecules gives us the blue sky we see every day, in most places around the world.

It is an elastic type of scattering because the photon energies remain unchanged and are more effective at short wavelengths i.e. the blue end of our visible spectrum. As light from the sun is scattered down to earth at a large angle, the light direction from the sun is largely in the blue end of the spectrum.

However, when we look at the sky nearer the sun’s position, the blue sky becomes a white glare. Also when we observe the sky furthest away from the sun’s position on the horizon, the blue is more saturated. This is where Mie scattering takes effect.

Mie Scattering

This is a physical phenomenon related to Rayleigh scattering, and whilst separate, it is not independent. Rayleigh scattering occurs when light scatters due to tiny particles in the air. They are 10 times less then the wavelength of light and blue light is scattered more than red light. In Mie scattering, the particles are always larger and instead of light being scattered in all directions, more light is scattered backwards rather than forwards.

When observed, the scattering effect looks rather like an antenna protruding in one direction. Instead of light scattering in all directions, Mie scattering moves mostly backward and is responsible for the white glare effect we see around the sun. To explain this in more detail, we must bring in Maxwell’s equations to provide solutions for scattering, where the phase of the incident signal can alter hugely within the dimension of the scattering particle.

Maxwell’s equations are solved in spherical co-ordinates through the separation of variables. The partial differential equations provide the mathematical model for optical, radio and electric technologies and are the foundation of classical electromagnetism. They help to understand Mie scattering when the mathematical model is expressed for optics.

The equations tell us how magnetic and electric fields are generated by currents, charges and field change. They show us how changing electric and magnetic fields spread at a constant speed in a vacuum. The solutions for scattering these equations have come to be known as the Mie solution, which is an infinite series of multipole expansion of the polarization in a spherical medium due to an incident wave; Mie scattering. When shown in diagrammatical form, Mie scattering is directive in nature and can also be expressed as a combination of varying orthogonal modes.

Smoke, raindrop particles and dust are all regular causes of scattering to spreading waves following the Mie solution. Mie scattering shows us why we see a glare around the sun and why some clouds are grey and others white.

Sources

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John Allen

Written by

John Allen

John is an award-winning writer and speaker. He holds a BA Hons. in Theological Studies from the University of Exeter as well as diplomas from the London School of Journalism and the Open University. John has worked in both the healthcare and digital sectors researching and writing about the latest developments in life sciences, robotics, space exploration, and nanotechnology.

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