By Tony Klein, Emeritus Professor with the School of Physics, University of Melbourne.
Did you guess the answer? If not, you’ll kick yourself: It’s simpler than you think! You were misled by the unwarranted assumption that the axis of polarisation was along one of the sides of the square. No! The polarisation axis was simply at 45° to the sides. It was cut out of a sheet of ordinary polaroid, at 45° to the sides and behaves as shown in the diagrams a), b) and c) below.
51-3 quizz answer
A similar “trick” is used by optometrists at the final stage of testing for astigmatism. A test object in the form of a ¼ diopter cylindrical lens, with its axis at 45° to the vertical, is inserted into the test lens and is flipped about its vertical axis to find out which position gives a clearer image (Is this better or worse?), thereby adding or subtracting a ¼ dioptre of cylindrical correction to the prescription of the test lens. Look out for it next time you get your eyes tested!