It is possible to polarize light in two different directions - let's say horizontal and vertical. Polarizing light is pretty easy to do - just pass it through a polarizing filter that is oriented either horizontally or vertically. We won't worry about the properties of the electromagnetic waves, here, but instead focus on the quantum mechanics of polarized photons. Let's suppose that a photon which is horizontally polarized is in state [h), and one which is vertically polarized is in state |v). In general, the photon can be in a superposition of both states, ly) = alh) + blo). Experimentally, this is easy to do - just rotate the polarizing filter at an angle. Let's go through a series of experiments to explore the quantum nature of polarized light. 1. Let's start with the basics. First pass unpolarized light, consisting of 100 photons, through a horizontal filter. (a) What state will the photons be in after that? (b) Next, we'll pass that light through a second horizontal filter. How many photons will pass through this filter? (c) Finally, the photons are then passed through a vertical filter. How many photons will pass through this filter? 2. Now we prepare a single photon in the state ly) = 1h) - 2/0). (a) Is this state normalized? If not, write out the properly normalized state. (b) If you pass this photon through a horizontal filter, what is the probability that it will go through? What about through a vertical filter