#5) 3D Glasses In order to create the illusion of depth on a flat movie theater screen, different images need to be fed to each eye. The first 3D glasses did this with color filters, red and blue, but those messed with the color of the movie. Later glasses used linearly polarized light, but those had the drawback that if you tilted your head, the two images would start to bleed into each other (at both eyes see both images equally). Modern 3D glasses use circularly polarized light, the two eigenstates of the Y Pauli operator. These glasses still use a linear polarizer, but the light first passes through a "quarter wave plate" which delays the light wave by a quarter of a wavelength in one direction. This amounts to multiplication by i. Assuming that Q is aligned to delay the vertical component of the incoming wave: 1The delay is the roughly the same for all light, so only one frequency is actually delayed a quarter of a wavelength. As a result, combinations of quarter-wave plates and polarizers produce lots of unexpected colors. 2-[ii] So modern circular polarization" lenses are a quarter-wave plate, which is a unitary operation that changes the incoming light, followed by a linear polarizer, which performs a projective measurement. a) What do the states |L) and (R) become after passing through the quarter-wave plate? b) At what angle should the linear polarizers be aligned in front of each eye to only permit the initially L) or (R) photons to get to that eye? c) If you had two pairs of 3D glasses, how could you show that the linear polarizers are located on the side of the lens closer to the eye? d) What is the probability of a linearly polarized state, 19), getting through each lens? If you wore the modern "circularly polarized" lenses to an old "linearly polarized" theater, what would the movie look like?