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Unformatted text preview: 1 Physics 316 Solution for homework 8 Spring 2005 Cornell University I. EXERCISE 1 As discussed in class, you send a vertically polarized beam through a tilted x /y analyzer, where the tilted y axis makes an angle of to the vertical. If you send one beam through an ideal horizontal polarizer afterwords you get a probability P 1 for transmission. If you now place the horizontal polarizer behind the other beam that comes out of the x /y analyzer, the probability for transmission is P 2 . Show that P 1 = P 2 for all . P 1 P 2 The transmission amplitude in a x /y analyser for the output states | x i and | y i is h x | y i = sin and h y | y i = cos respectively. If a horizontal polarizer is placed at the output of the x /y analyser, the transmission probability is now P 1 = |h x | x ih x | y i| 2 and P 2 = |h x | y ih y | y i| 2 for the two possible outputs of the analyzer. Since h x | y i = sin and h x | x i = cos , we get finally that P 1 = P 2 = sin 2 cos 2 . II. EXERCISE 2 How can a right circular polarized light beam be changed to a left circular light be with as little loss of intensity as possible ? A right-circularly polarized light beam can be expressed as the sum of a linearly polarized light beam in x direction and a linearly polarized light beam in y direction, the later with a phase shift of- / 2. A left circularly polarized beam can be expressed the same way, but with a phase shift of / 2. To convert one into another, it suffices to give a phase shift of to the y component. Thus, we only need to let the light beam go trough two / 4-plates. III. EXERCISE 3 Given a photon beam in polarization state which is a pure but unknown state of liner or circular polarization. It is not known whether it is right or left handed nor is the direction of linear polarization known. Specify a method by which you can determine the polarization state. What is the maximum number of measurements that will be needed to determine the state ?...
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