As a photographer, I have always wondered why the light reflecting off water, foliage and glass is affected by polarising filters, but the light reflecting off metal surfaces is not.
鈥� The fundamental reason for the difference is the way the free electrons in the metal interact with light waves. The key to understanding this is Fresnel鈥檚 equations, which describe how much light is reflected by a material based on its refractive index.
鈥淔resnel鈥檚 equations describe how much light is reflected by a material using its refractive index鈥�
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These calculations depend on the polarisation of light in two planes: perpendicular to the plane of incidence (鈥渟鈥�) and parallel to it (鈥減鈥�). The equations predict that at a particular angle, known as Brewster鈥檚 angle, the amount of 鈥減鈥� polarised light will fall to a minimum.
For glass, transparent plastics and water the refractive index is between 1.33 and 1.6. This leads to a Brewster鈥檚 angle of between 50 and 60 degrees, causing the 鈥減鈥� reflectivity to drop to zero. So if your filter blocks the 鈥渟鈥� wave, you will see no reflection at all.
For metals, it鈥檚 more complicated. The refractive index becomes a 鈥渃omplex鈥� number, with real and imaginary parts. The imaginary part describes how strongly the metal absorbs light and is a very large number.
When plugged in to Fresnel鈥檚 equations, this also makes the Brewster鈥檚 angle large, up to around 85 degrees. The reflection of the 鈥減鈥� polarisation only dips a little, maybe to 74 per cent, so the filter wouldn鈥檛 produce a strong contrast.
Foliage, of course, is a complex mix of materials. It contains a lot of water, doesn鈥檛 have many free electrons, but it does absorb light. Its refractive index isn鈥檛 easy to calculate, but will be between that of water and a metal. It would have a significant imaginary part to the index, but much smaller than for a metal. So one would expect the effect of the filter to be weaker on leaves.
Harvey Rutt, Southampton, UK
This article appeared in print under the headline 鈥淔iltered water鈥�