For those who don't want to bother with the link, the question was this. Two polarizers rotated 90° from each other don't transmit light. Yet inserting a third in between at 45° from each allows some light to pass. Why?
The answer you cite is ok, although it gives a somewhat false picture of how polarizers work at a microscopic level. I'll try to do better, and shorter.
Let's delay discussing how polarizers work. The point is that they block all light whose electric fields are along some direction, say vertical, while allowing most light with electric fields at right angles to that to pass. So if the first polarizer lets horizontally polarized light (call it 0°) through and the second only lets vertically polarized light (90°) through, nothing gets through.
What happens when you insert that 45° polarizer in between? The key point is that the horizontal fields that hit it can be expressed as the sum of 45° fields (transmitted) and 135° fields (blocked). That's the same as how you can express a move northeast as a sum of a north move and an east move. The 45° fields that hit the 90° (vertical) polarizer can be expressed as the sum of 90° fields (transmitted) and 0° fields (blocked).
Now let's ask how a polarizer can work. It's easiest to see for long-wavelength radiation, say microwave, whose interaction with matter can sometimes be treated classically, rather than for the quantum interactions of visible light and matter. Take a grid of lots of closely spaced horizontal wires, not quite touching. They can carry electric currents horizontally but not vertically. A vertical microwave field will pass right through the grid. A horizontal one will drive currents in the wires, which heat them up, pulling energy out of the wave. With a few layers of these wires, the horizontal wave is blocked. For visible light the picture isn't right but in effect the orientation of the transition dipoles accomplishes the same thing.
(published on 02/07/11)