At any photography store one can buy polaroid filters. These serve to polarize light. From Maxwell, we know that light has both electric and magnetic parts, called fields, that vary in space and time, in a wavelike manner. These two fields are perpendicular to one another, eg one might ``wave'' vertically as it moves forward, and the other horizontally, the first like a jumprope being waved up and down, and the other like a snake slithering through the grass. A polaroid filter has very fine parallel lines that are sensitive to the electric field, so that any light ``bundles'' that pass through it must come out with their electic fields parallel to those lines; the light that passes through is said to be polarized, eg in the vertical direction. (The filter does not directly affect the magnetic field, which simply goes along with whatever the electric field does.) Also, we can rotate the filter, and thus make it a horizontal polarizer, a 45-degree slanted polarizer, etc. Here is a diagram of light passing through a vertical polarizer:
-----
ordinary randomly | ^ | vertically polarized
polarized light ===> | | | ===> light (50% of the light gets through)
| v |
-----
vertical filter
If we now place a second filter after the first, also vertically polarizing, all the vertically polarized light coming out of the first filter passes through the second as well, and remains unchanged (vertically polarized). On the other hand, if we rotate the second filter 90-degrees to make it a horizontal polarizer, no light from the first filter passes through the second at all. This does not surprising at this point.
What does seem surprising is the amount of light that gets through the first polarizer (whether or not there are other polarizers after it): fully 50% of the light that comes in on the left comes out on the right. This seems odd: for that incoming light is random, eg just from lightbulbs overhead, and presumably oriented in all possible directions. So it would seem that only a tiny fraction should pass through: those few bundles that happened to have their electric fields already vertical. Maybe something special about the lightbulbs has polarized 50% of them in advance? But if we rotate the filter, by any angle, we still get 50% coming through.
It seems clear that the filter is somehow changing the incoming light, polarizing 50% of it vertically. What is more, the light that does not get through not only bounces off the filter but itself is polarized in the horizontal direction! So all of the original light is affected by the filter and ends up in one of two states: vertical or horizontal. But then why does no vertical light get through a horizontal filter? There seems to be a pattern of sensitivity to the direction of polatization of the incoming light. This then might explain the 50% result for random polarization: if lots of light bundles come in with polarizations in lots of more or less uniformly varied directions, then some get through because they already have the right (vertical) polarization, some do not get through at all (horizontal) and most get through with varying probabilities.
There is a second somewhat curious feature: if we again place a second filter after the first, but with a 45-degree rotation, 50% of the light that passes the first filter will succeed in passing the second, ie 25% of the original light gets through both. And if we then place a third horizontal filter after these, 50% of the light coming to it gets through, ie 12.5%. But if we already agree that filters can change the polarization of incoming light, then this is not so surprising, except that we do not have an explanation yet for why the particular amounts pass through - that will come later, and turns out to be a far more general issue than that of light and filters.
Finally, if we again do the dimming trick, we still get the same results: half the bundles get through the first filter, etc, except now we have to wait a long time. In any one hour there is only one bundle, and it either gets through or it doesn't, and on average 50% go each way; and each ends up polarized vertically if it passes, and horizontally if it doesn't.