If you take two crossed polarizers (for example, a horizontal and vertical one), no light will get through them. Yet when you insert a third polarizer between the two, oriented diagonally, then some photons make it through. How does adding that polarizer (which will block some photons) cause photons to get through?

Say that the first polarizer is horizontal. Any photons that make it through that one are then horizontally polarized. If the vertical polarizer comes next, it will block all of these photons. When the diagonal polarizer is in place, however, it will let half of them through and these transmitted photons will then be diagonally polarized. When these diagonally polarized photons arrive at the vertical polarizer, now half of them will get through—they have no "memory" of ever having been horizontally polarized.

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