‘n’ polarizing sheets are arranged such that each makes an angle $45^{o}$ with the preceeding sheet. An unpolarized light of intensity I is incident into this arrangement. The output intensity is found to be $\frac{I}{64}$ . The value of n will be:

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Detailed Solution

$\begin{array}{l} I^{'} = \frac{I}{2} {(\cos^{2} 45)}^{n - 1} \\ I^{'} = \frac{I}{64} \\ \frac{I}{64} = \frac{I}{2} {(\frac{1}{2})}^{n - 1} \\ \frac{1}{2^{n - 1}} = \frac{1}{32} \end{array}$
$n = 6$

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