What it shows:
Polaroid filters absorb one component of polarization while transmitting the perpendicular components. The intensity of transmitted light depends on the relative orientation between the polarization direction of the incoming light and the polarization axis of the filter and is described quantitatively by Malus' cos2θ intensity law.
How it works:
The demonstration apparatus is identical to that for the Polarization by Absorption demonstration.
The Polaroid sheet in front of the light box (polarizer) and the (analyzer) Polaroid sheet are oriented so that their transmission axes are 90° with respect to each other. No light is transmitted by the analyzer -- no surprise. But now one adds a third Polaroid sheet between the polarizer and analyzer with its transmission axis oriented obliquely to the other two. The question is, does any light now emerge from the analyzer? Malus' law predicts that light will now emerge and the experiment confirms the prediction. Without the vector component analysis, it seems paradoxical that one can produce less absorption by the addition of more absorbers. Of course the paradox is resolved by the fact that these are selective absorbers, absorbing only the light whose polarization direction is perpendicular to its transmission axis.
Setting it up:
Same as the Polarization by Absorption demonstration.
One could confirm Malus' law with just two Polaroid sheets (the polarizer and analyzer) and measure (with a light meter) the light intensity emerging from the analyzer as a function of angle. However, clear-cut quantitative results are spoiled by the fact that the analyzers are not perfect (significantly less than 50% transmission of unpolarized light) and this systematic error muddies the results. The three-polarizer experiment is a much more interesting way of demonstrating the effect, particularly if presented as a puzzle. For example, begin by inserting the third polarizer so that its axis is parallel with the first polarizer. Remove it and reinsert it parallel to the second (analyzer) polarizer. In both cases, nothing happens because the third polarizer is redundant to the first or second. Then surprise the audience by inserting it obliquely at 45°.