Physics - Wave Optics Question with Solution | TestHub

Let the initial intensity of the unpolarized light be $I$.

When unpolarized light passes through the first polarizing sheet, its intensity becomes half. Thus, the intensity after the first sheet is:
$I_1=\frac{I}{2}$

For the subsequent sheets, the light is already polarized. According to Malus's Law, when polarized light passes through a polarizer at an angle $\theta$, the transmitted intensity is multiplied by ${\cos }^2\theta$.

Since each of the remaining $(n-1)$ sheets makes an angle of $45^{\circ }$ with the preceding one, the intensity after passing through the $n$-th sheet is:
$I_n=I_1({\cos }^{2}45^{\circ }{)}^{n-1}$

Substituting $I_1=\frac{I}{2}$ and $\cos 45^{\circ }=\frac{1}{\sqrt{2}}$:
$I_n=\frac{I}{2}{\left(\frac{1}{\sqrt{2}}\right)}^{2(n-1)}$

$I_n=\frac{I}{2}{\left(\frac{1}{2}\right)}^{n-1}=\frac{I}{2^n}$

We are given that the final output intensity is $\frac{I}{64}$. Therefore:
$\frac{I}{2^n}=\frac{I}{64}$

$2^n=64$

$2^n=2^6\Rightarrow n=6$

Answer: $6$