1. (20 points) Create the following setup in your own workspace. (a) Using only polarizing filters (the second element under the Polarization section) create a configuration such that the detector only detects 6% of the initial photons. What is the minimum number of polarizing filters required to achieve this? (b) Describe a general strategy using only polarizing filters that causes the detector to detect only n% of the initial photons. You may assume n100 and n=2k100 with kZ+. (c) There is only one path in this configuration so we can use statevectors to represent the polarization of the photons. Let 0=(10) represent photons completely oriented in the horizontal direction. Similarly, let 1=(01) represent photons completely oriented in the vertical direction. Note we can characterize any state of these bases by a single parameter as follows: =cos0+sin1. Assume the photon source outputs photons completely oriented in the vertical direction. Suppose the matrix M represents a polarizing filter oriented in the vertical direction. Answer the following questions. - What does M0= - What does M1= Give the matrix for M= d) Given some state , what is the probability, in terms of , that the photon will pass through a vertically oriented filter? (e) Does applying a vertical filter, then a horizontal filter, and then a filter oriented 45 degrees from the origin produce the same result as applying a vertical filter, then a filter oriented 45 degrees from the origin, and then a horizontal filter? Why or why not