Question

Unpolarized light of intensity $I_0$ is incident on a series of three polarizing filters. The axis of the second filter is oriented at $45^{\circ }$ to that of the first filter, while the axis of the third filter is oriented at $90^{\circ }$ to that of the first filter. The intensity of the light transmitted through the third filter is $\frac{I_0}{n}$. Find $n$.

Answer 1

Answer: 8

The first filter always reduces the intensity of the light to half, $I_1=1/2I_0$
The next filter reduces the intensity by $I_n=I_{(n-1)}{\cos }^2\theta$.
$\theta$ is the angle with respect to the $n^{\text{th }}$ filter.
Thus,