|MadSci Network: Chemistry
The simplest answer is that the brown color acts as a filter for light which might otherwise stimulate a chemical reaction causing the material being stored in the bottle to decompose, deteriorate, or change form by what is called an oxidation-reduction reaction.
Check out this website to see the types of "damage" that can be done by light: http://www.nedcc.org/plam3/tleaf24.htm
Another interesting website shows the relationship between light and color changes in glass: http://library.kcc.hawaii.edu/external/chemistry/everyday_photo_oxid.html
Finally, check out this website to see the relationship between light and photography: http://www.cheresources.com/photochem.shtml
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