Light will not pass through a pair of Polaroid sheets when they are aligned perpendicularly. However, if

Question:

Light will not pass through a pair of Polaroid sheets when they are aligned perpendicularly. However, if a third Polaroid is sandwiched between the two with its alignment halfway between the alignments of the other two (that is, with its axis making a 45° angle with each of the other two alignment axes), some light does get through. Why?