Answer
The intensity of the transmitted light is: $~I_0~cos^2 \theta_1~cos^2(\theta_1-\theta_2)$
Work Step by Step
We can use Malus' law to determine the intensity of the light after passing through the first polarizing sheet:
$I_1 = I_0~cos^2~\theta_1$
The angle between the two polarizing sheets is $\theta_1-\theta_2$. We can find the intensity of the light after passing through the second polarizing sheet:
$I_2 = I_1~cos^2(\theta_1-\theta_2)$
$I_2 = I_0~cos^2 \theta_1~cos^2(\theta_1-\theta_2)$
The intensity of the transmitted light is: $~I_0~cos^2 \theta_1~cos^2(\theta_1-\theta_2)$
