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I Malus' law in the limit of infinitely many polarizers

  1. Sep 5, 2016 #1
    Hi.

    How can I prove
    $$\lim_{n\to\infty} \cos(\alpha/n)^{2n}=1$$
    for all ##\alpha\in\mathbb{R}##? The physical background is Malus' law for perfect linear polarizers, I'd like to show that one can losslessly rotate a linearly polarized wave by any angle by stacking an infinite number of infinitely rotated polarizers.
     
  2. jcsd
  3. Sep 5, 2016 #2

    mathman

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    Rough proof: [itex](cos(\alpha /n))^{2n}\approx (1-\frac{\alpha^2}{2n^2})^{2n}\approx e^{-\frac{\alpha^2}{n}} \to 1[/itex]
     
  4. Sep 6, 2016 #3
    You can take the log and use L'H rule.
     
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