Question

In above figure, a beam of un-polarized light, with intensity $43W/m^2$, is sent into a system of two polarizing sheets with polarizing directions at angles ${\theta }_1={70}^0$ and ${\theta }_2={90}^0$ to the $y$ axis. What is the intensity of the light transmitted by the system?

Answer 1

In this case, we replace $I_0{\cos }^2{70}^0$ by $\frac{1}{2}{I}_0$ as the intensity of the light after passing through the first polarizer. Therefore,
$I_f=\frac{1}{2}{I}_0{\cos }^2({90}^0-{70}^0)=\frac{1}{2}\left(43W/m^2\right)\left({\cos }^2{20}^0\right)=19W/m^2$.