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  4. ' n ' polarizing sheets are arranged such that each makes an angle 45° with the preceeding sheet. An unpolarized light of intensity I is incident into this arrangement. The output intensity is found to be I / 64. The value of n will be:

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

JEE MainJEE Main 2023Wave Optics

Solution:

After passing through first sheet
$I_1=\frac{I}{2}$
After passing through second sheet
$I_2=I_1 \cos ^2\left(45^{\circ}\right)=\frac{I}{4}$
After passing through $n^{\text {th }}$ sheet
$ I_{ n }=\frac{I}{2^{ n }}=\frac{I}{64} $
$ n=6$