|MadSci Network: Physics|
Greetings from St. Louis, MO, USA, Karthik! :) I've put all the links for my answer at the bottom of this page. Please take a look at them as you read. The "simple" answer to why we can't see though a fog /smoke / cloud of smoke is: Fog and smoke are made of "particles" of water, or hydrocarbons, as well as the usual atmospheric gases. These particles redirect, or, "scatter" light rays. If there are a great number of particles in a fog, or cloud of smoke, light rays get scattered randomly, and, therefore, carry no useful information about what is behind, or in the cloud, to our eyes. You ask if this can be quantified, though, and that's where the "simple" part of this ends and a beautiful complexity creeps in. (This is an AMAZING question, Karthik!) Yes, it can be quantified, but the math gets pretty tough! You see, the scattering of light is dependent upon the wavelength of ambient light, the size and density of the "target" particles in the cloud (or, smoke cloud), and the properties of the particles themselves. (Smoke particles are different from the water droplets we would find in fog, or a cloud. In fact, "smoke" can be made up of so many different things I think I'll just stick to general theory, and leave the detailed calculations to you!) In 1906 a gentleman named Gustav Mie published a theory about the scattering of light by transparent spheres. This is applicable to water droplets, because water droplets are pretty much "transparent spheres", so it's a good way to think about the way light is scattered by clouds and fog. "Mie Scattering" is accepted as the reason clouds and fog appear white in color. Basically, the droplets of water in a cloud (or fog) are much greater in size than the wavelength of incident light rays. Reflection and diffraction are important considerations, along with the size and distribution of water droplets in the particular cloud you are looking at. (My understanding is something like 96% of light gets scattered "forward", or normal to the direction of propagation of a light beam. Roughly 4% of the light beam seems to get reflected back along the path of incidence. Don't put much stock in these numbers, though, as there are a lot of different factors involved here! For example: water droplets may not be exactly "spherical" if they are blown about by the wind, or, if they are distorted by triboelectric [static electricity] forces, and gravity.) "Rayleigh Scattering" is sort of a subset of Mie's thinking, because fewer variables are considered. Rayleigh scattering concerns scattering of light by particles smaller than the wavelength of the incident light ray. This is generally accepted as the reason the sky is blue, and a sunset appears red…both of which might be going on around the smoke, cloud, or fog you are looking at! When we speak of "fog", or "smoke" we are talking about "real-world" phenomena. We have some pretty good mathematical models of what's going on, but each case is different, because what we are seeing is essentially "non-linear", or, "chaotic". These are the really "cool" topics in science, I think! (Fractals are non-linear. Fog is kind of fractal, in a way! Really cool stuff, if you think about it, and beautiful to look at, too!) To make a good model of what goes on between light and fog, or, smoke, you need to plug a bunch of equations into a computer and let them churn around a bit. (To do this REALLY well, it helps to have access to a supercomputer! See links, below.) Interestingly, a lot of thinking in the "VRML world" is directed toward accurately representing the answer to your question. You might want to investigate that. I hope I've answered your question, Karthik. If not, I hope I've at least pointed you in the right direction! Either way, I'd like to know more about this, so, if you have more questions, or, if you disagree with my answer, please feel free to e-mail me at firstname.lastname@example.org. I like to help! Your MadSci, -Matt email@example.com Links: The basics of light, and why birds just don't understand it: http://www.us ers.mis.net/~pthrush/lighting/nature.html Basic Mie Scattering: http://c ovis.atmos.uiuc.edu/guide/optics/html/mie-scat.html You can say "Mie" in many ways: http://euromet.meteo.fr/external/demos/courses/glossary/miescatt.htm Everything you ever wanted to know about "Mie"(Look all the way back to the parent page. There's lots of good stuff about scattering here!): http://hyperion.gsfc.nasa.gov/Other/CDROM_Lectures/Lecture4/Text/X/ OVER**f1 2-18.html#Atmos Scat Another "must see" Mie site: http://www.photometer.c om/en/abc/abc_110.htm A Mie Scattering calculator you can drive: http://www.uni-jena.d e/~phb/Jamie/MiePlot.html Examples of Mie Scattering as seen with a supercomputer: http://www.ait .nrl.navy.mil/people/cole/examples.html Another way to use compters to calculate Mie Scattering: http://lu t.ac.uk/departments/el/research/optics/mie95.html A VRML way to fog up your computer(See the whole site. It's cool!): http://www.informatik.unibw-muenchen.de/SCS/confernc/wmc98/websim/v rml/file s/vrml97/slides/fog.htm The view from above: htt p://orbit-net.nesdis.noaa.gov/arad/fpdt/2_partit/scatter.html Okay, you asked "Mie"!: htt p://equinox.comnet.unr.edu/homepage/daved/nmsu/mietheory.html How clouds and fog happen (Pictures here. Check out the whole site!): http://www.usatoday.com/ weather/wwater0.htm More about types of fog,and how it happens: http://www.touchtmj4.c om/weather/fogtypes.htm
Try the links in the MadSci Library for more information on Physics.