Optical Properties of Matter Rayleigh Scattering

Questions to be answered: Why are clouds usually white (or grey) Why can’t we usually see the beam of light on its journey from a laser or a torch? The colour of the sky depends on the size and composition of the particles forming it and the interaction between them and the photons of light. The light that is absorbed (which will only happen if close to the resonant frequencies of the electrons) and is then re-emitted at the same frequency is called scattered light. This scattering process is known as Rayleigh Scattering. Why is the sky blue?

Interesting things happen as light rays enter our atmosphere from the sun. As the light enters the earth’s atmosphere it hits many small air molecules. In our atmosphere (made up of 78% Nitrogen, 21% Oxygen and 1% Argon) most of the scattering particles are very small. When the light reaches your eye from the scattering particles, you see light coming from all directions. The scattered light is emitted by the particles in our atmosphere. Without these particles our sky would be dark. Outer space is dark because there are no particles to scatter light. The air molecules are bombarded with electromagnetic waves with a wide range of wavelengths. The photons with frequencies close to the resonant frequencies of the orbiting electrons are absorbed by the electrons. These electrons then re-emit the electromagnetic waves as photons of the same wavelength (colour), but in random directions. For example if we have a vibrating paddle in a pool, it will create water waves. Like the vibrating paddle, the particles create waves that pass through space. Not all particles in the atmosphere re-emit the light in the same way. Small particles re-emit light equally in all directions (A). This is Raleigh Scattering. Larger particles focus the light mostly in the direction opposite that of the sun (D). This is not due to Rayleigh Scattering. The other two types are called Mie and Raman scattering, but are off the syllabus

Particle Size Matters Very short wavelengths of light are best scattered by small particles (the size of a Nitrogen Molecule). In our mostly Nitrogen filled atmosphere, blue light is scattered the most because it is closest to the natural frequency of nitrogen molecules. This is why our sky is blue. Have you ever seen a brilliant red sunset? The reds are found close to the horizon because here the sunlight travels through the greatest amount of the atmosphere and therefore passes through many particles before reaching us. Where on the horizon are the red colours found? The percentage of blue, green, yellow and orange photons in the light beam decreases the further the beam passes through the atmosphere, so our brain interprets the colour as shifting towards the red as the other colours have been scattered. Blue is scattered the most as it has the shortest visible wavelength. White light minus blue light appears orangey-red to us.

Why is the Sky BLUE?  The blue colour of the sky is caused by the scattering of sunlight off the molecules of the atmosphere. This scattering, called Rayleigh scattering, is more effective at short wavelengths (the blue end of the visible spectrum) because blue light has a high frequency close to the resonant frequency of the electrons orbiting the nitrogen molecules. Therefore the light scattered down to the earth at a large angle with respect to the direction of the sun's light is predominantly at the blue end of the spectrum.

If you drive through a patch of fog at night you will know that before reaching the fog, the headlights are barely visible to the driver and passengers, but as soon as you progress into an area of fog, the fog is lit up and your visibility range decreases dramatically. If you drive through a patch of fog at night you will know that before reaching the fog, the headlights are barely visible to the driver and passengers, but as soon as you progress into an area of fog, the fog is lit up and your visibility range decreases dramatically. For the same reason that the fog droplets are white when you shine car headlights at them. When the particles are large (water droplet size) all of the light is scattered equally. We see white light scattered when there are water or ice crystals in the air. Each wavelength of visible light scatters the same amount when the light hits the water droplets. This phenomenon is not due to Rayleigh Scattering - it is known as Mie scattering)! You will no doubt remember that you can’t see the path of a laser beam unless there are dust particles in the air to scatter the light. I’ve demonstrated this to you with Lycopodiumpowder. For the same reason that the fog droplets are white when you shine car headlights at them. When the particles are large (water droplet size) all of the light is scattered equally. We see white light scattered when there are water or ice crystals in the air. Each wavelength of visible light scatters the same amount when the light hits the water droplets. This phenomenon is not due to Rayleigh Scattering - it is known as Mie scattering)! You will no doubt remember that you can’t see the path of a laser beam unless there are dust particles in the air to scatter the light. I’ve demonstrated this to you with Lycopodium powder. Because of the presence of the fog droplets, you can no longer see very far in front of your car. The cone shaped area that is lit up the most is directly in front of your headlights. This occurs because the water droplets in the air scatter the light. Why do clouds appear white? Why do clouds appear white?

Rayleigh Scattering Clouds, in contrast to the blue sky, appear white to grey. The water droplets that make up the cloud are much larger than the molecules of the air and the scattering from them is almost independent of wavelength in the visible range. All of the visibile light is scattered, so we see the colour of the light entering the clouds. Clouds acquire the colour of the light entering them – this is why the clouds are orangey-red at sunset.

Rayleigh Scattering Rayleigh scattering refers to the scattering of light off of the molecules of the air, and can be extended to scattering from particles up to about a tenth of the wavelength of the light. It is Rayleigh scattering off the molecules of the air which gives us the blue sky. Lord Rayleigh calculated the scattered intensity from dipole scatterers much smaller than the wavelength to be:

Rayleigh Scattering – some questions 1.Write down the Rayleigh Scattering formula that equates Intensity (I) with wavelength 2.Explain briefly why when looking up (away from the Sun) at the sky it appears blue rather than red or white. When sunlight reaches our atmosphere, certain wavelengths are absorbed and then re- emitted (scattered). According to the Rayleigh Scattering, shorter wavelengths (the blue end of the spectrum) will be scattered much more strongly than the longer wavelengths, so we see the blue light scattered down to us. The blue light is nearer the resonant frequency of the electrons in the dust particles. 3.Mars has an atmosphere rich in carbon dioxide. Suggest a reason for the observed fact that the sky on Mars in red rather than blue. When sunlight reaches Mars, certain wavelengths are absorbed and then re-emitted (scattered). Carbon Dioxide molecules are larger than nitrogen molecules and so the electrons have a lower resonant frequency than those of nitrogen moleucles. The electrons shared in Carbon Dioxide molecules have a resonant frequency nearer the red end of the spectrum and so the red light will be scattered more than the blue light.

In optical fibres, one of the major limitations in selecting the wavelengths to use is the amount of light scattered by Raleigh Scattering. Since the amount scattered depends on 1/ 4 the shorter wavelengths will not travel very far down the fibre without being scattered out of the fibre. With the current materials used, Rayleigh Scattering considerations tell us that wavelengths shorter than about 15 x m will begin to be scattered. This wavelength is in the near infra-red part of the spectrum. Wavelengths in the visible part of the spectrum (4 ~ 7 x m) will thus be scattered far too much for practical use in long distance telecommunications. 4. Given that the wavelength of Blue light is about 4 x m and red has a wavelength of about 7 x m, calculate the ratio of the intensity of RED to BLUE light that is transmitted through air. What is the significance of the result? This means that over nine time as much red light is transmitted per unit length than blue light through the material.

The END ! NPY April 2008