Exercise 2.1

$\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\mathbf{Exercise\ 2.1}$

Let the direction $\ket v$ of polaroid $B$'s preferred axis be given as a function of $\theta$, $\ket v = \cos\theta\ket\to + \sin\theta\ket\uparrow$, and suppose that the polaroids $A$ and $C$ remain horizontally and vertically polarized as in the experiment of Section 2.1. What fraction of photons reach the screen? Assume that each photon generated by the laser pointer has random polarization.

page revision: 1, last edited: 12 Nov 2011 04:40

The fraction $0.5$ of photons that pass $A$ and are in state $\ket{\rightarrow}$. The projection of $\ket{\rightarrow}$ onto the preferred axis of $B$ is $\cos \theta$ so $(\cos \theta)^2$ of the photons pass $B$ and are in state $\ket{v}$. The projection of $\ket{v}$ onto the axis $\ket{\uparrow}$ of $C$ is $\sin \theta$. Thus, overall $0.5 (\cos \theta)^2 (\sin \theta)^2$ of the photons reach the screen.

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