Another type of scattering

Clouds are mists drawn up by the heat of the sun, and their ascension stops at the point where the weight they have gained is equal to their motor power
– Leonardo da Vinci

The weather has changed outside. We had almost a week of beautiful but cold, sunny days. Now, clouds have rolled in, changing the sky from beautiful blue to drab gray. Have you ever looked up at a cloudy sky and wondered why the clouds are white? Alternately, have you ever looked at the foam of a dark beer and wondered how the foam could be white while the beer is dark? The answer lies in how light interacts with water droplets in clouds and tiny bubbles in beer foam.

The average size of a water droplet is between 0.01 and 0.02 mm, with the largest ones about 0.15 mm (from ‘The Field Guide to Natural Phenomenon’ by Keith Heidorn and Ian Whitelaw) and they are transparent. Cloud colour results from an optical phenomenon. Since water droplets are similar in size to visible light wavelengths, when light passes through the water droplets all wavelengths are affected the same way. This optical phenomenon is very different to the preferential blue scattering from gas particles in Rayleigh scattering that make the sky appear blue. The effect of scattering each wavelength of light in the same way is called Mie scattering after Gustav Mie, the German physicist who figured this out (there are others who independently came to the same conclusion but didn’t get the phenomenon named after them). In Mie scattering all wavelengths scatter equally, making clouds appear white since all the wavelengths are present in the same amounts. In a thick bank of clouds, no direct light makes it through; instead all colour results from diffuse radiation. Thick clouds may appear in menacing shades of gray.

The foam atop of a freshly poured beer is composed of uniformly sized bubbles suspended in beer (from ‘Does Anything Eat Wasps? And 101 Other Questions’ edited by Mick O’Hare). Each tiny bubble is filled with air with a lower refractive index than the liquid around it. As a result, the bubbles act like magnifying glasses in reverse, where light that enters the bubbles is scattered in different directions – another example of Mie scattering. Reflections off the bubble’s surface adds another layer of scattering. Both scattering effects created by each bubble is compounded in the foam. Since each wavelength of light is affected the same way, the fraction of light that makes it out will appear white, that is all wavelengths are equally present (The end result might be slightly yellow if the beer surrounding the bubbles absorbs some of the light).

Light hitting dust, smoke or pollen can also experience Mie scattering. This effect also explains why milk is white.

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