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.