Two crossed polaroids, oriented vertically and horizontally, are placed in front of a goose-neck lamp, thereby preventing light from passing to the viewers. When a third polaroid is inserted between the two crossed polaroids at an angle of 45 degrees with respect to the original axes, light can be seen passing through the system.
This demonstrates that the electromagnetic field of which the light consists is a vector. The diagonal polaroid passes a component at 45 degrees with respect to the original light, and the second polaroid passes a component at 45 degrees with respect to the diagonal polaroid. The component of a component is actually perpendicular to the axis of the second original polaroid.
The real paradox involving this system involves an analysis of single photons. How can a single photon originally polarized parallel to the first polaroid have its angle of polarization rotated 90 degrees and exit the final polaroid polarized perpendicular to its original plane of polarization?
Compare M7-03, a simpler demonstration using only two polarizing filters.