Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 24 - The Wave Nature of Light - General Problems - Page 711: 86

Answer

31 polarizers

Work Step by Step

Let the initial intensity be $I_o$. The initial light is unpolarized, so the intensity after the first polarizer, $I_1$, will be half the initial intensity. $$I_1=\frac{1}{2}I_o$$ Use equation 24–5 to see what happens next. $$I_2=I_1cos^2\theta$$ We see that every polarizer after that reduces the intensity by a factor of $ cos^2 10^{\circ}$. Find the intensity after N polarizers, and set it equal to one-fifth of the original intensity. $$I_{N}=\frac{1}{2}I_o (cos^2 10^{\circ})^{N-1}=0.2I_o $$ $$N\approx30.93$$ Therefore, 31 polarizers are necessary for the intensity to be less than one-fifth of its original value.
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